Using nucleic acid size range for noninvasive cancer detection

ABSTRACT

Size-band analysis is used to determine whether a chromosomal region exhibits a copy number aberration or an epigenetic alteration. Multiple size ranges may be analyzed instead of focusing on specific sizes. By using multiple size ranges instead of specific sizes, methods may analyze more sequence reads and may be able to determine whether a chromosomal region exhibits a copy number aberration even when clinically-relevant DNA may be a low fraction of the biological sample. Using multiple ranges may allow for the use of all sequence reads from a genomic region, rather than a selected subset of reads in the genomic region. The accuracy of analysis may be increased with higher sensitivity at similar or higher specificity. Analysis may include fewer sequencing reads to achieve the same accuracy, resulting in a more efficient process.

CROSS-REFERENCES TO RELATED APPLICATIONS

The present application is a continuation application of U.S. patentapplication Ser. No. 16/178,378, entitled “USING NUCLEIC ACID SIZE RANGEFOR NONINVASIVE CANCER DETECTION,” filed Nov. 1, 2018, which claimspriority from and is a non-provisional application of U.S. ProvisionalApplication No. 62/580,906, entitled “USING NUCLEIC ACID SIZE RANGE FORNONINVASIVE PRENATAL TESTING AND CANCER DETECTION,” filed Nov. 2, 2017,the entire contents of each of which are herein incorporated byreference for all purposes.

BACKGROUND

The demonstration of the presence of circulating cell-free DNA (cfDNA)originating from the fetus in the blood plasma and serum of pregnantwomen (Lo et al., Lancet 1997; 350:485-487) has completely transformedthe practice of prenatal testing through the development of noninvasiveprenatal testing (NIPT). NIPT has an advantage in avoiding risksassociated with invasive tissue sampling, such as via amniocentesis andchorionic villus sampling (CVS). Thus far, NIPT has been used for fetalRhD blood group genotyping (Finning et al. BMJ 2008; 336:816-818; Lo etal. N Engl J Med 1998; 339:1734-1738), fetal sex determination forsex-linked disorders (Costa et al. N. Engl. J. Med. 2002; 346:1502),chromosomal aneuploidy detection (Chiu et al. Proc Natl Acad Sci USA2008; 105:20458-20463; Fan et al. Nature 2012; 487:320-324; Chiu et al.BMJ 2011; 342:c7401; Bianchi et al. N. Engl. J. Med. 2014; 370:799-808;Yu et al. Proc. Natl. Acad. Sci. U.S.A. 2014; 111:8583-8; Norton et al.N. Engl. J Med. 2015; 372:1589-1597) and diagnosis of monogenicdisorders (Lam et al. Clin. Chem. 2012; 58:1467-75; Lo et al. Sci.Transl. Med. 2010; 2:61ra91-61ra91; Ma et al. Gene 2014; 544:252-258;New et al. J Clin. Endocrinol. Metab. 2014; 99:E1022-E1030). Inparticular, using massively parallel sequencing of maternal plasma DNA,NIPT for common chromosomal aneuploidies has been rapidly adopted forclinical service in dozens of countries and is used by millions ofpregnant women every year (Allyse et al. Int. J Womens. Health 2015;7:113-26; Chandrasekharan et al. Sci Transl Med 2014; 6:231fs15).

In early validation studies (Chiu et al. BMJ 2011; 342:c7401; Sparks etal. Am. J. Obstet. Gynecol. 2012; 206:319.e1-9), NIPTs were performed onpatients at high-risk for aneuploidy, and high positive predictivevalues (PPVs) have been achieved from 92% to 100%. The relativeconcentration of fetal DNA in a particular maternal sample, commonlyreferred to as the fetal DNA fraction, is an important determinant ofthe accuracy of NIPT (Chiu et al. BMJ 2011; 342:c7401; Jiang et al.Bioinformatics 2012; 28:2883-2890, npj Genomic Med. 2016; 1:16013). Thesensitivity of trisomy 21 detection would be significantly decreasedwith a reduction in the fetal DNA fraction (Chiu et al. BMJ 2011;342:c7401; Canick et al. Prenat. Diagn. 2013; 33:667-674). Hence, falsenegative results for trisomy detection might occur in pregnancies withlow fetal DNA fractions. For example, Canick et al reported that among212 cases with Down syndrome, there were 4 false negatives, all of whichhad fetal DNA fractions were between 4% and 7% (Canick et al. Prenat.Diagn. 2013; 33:667-674).

It is important to note that for in a number of laboratories performingNIPTs, test failures or no-call results would be observed in aproportion of analyses. In some studies, the total laboratory failurerate could be as high as 8.8% (Porreco et al. Am. J Obstet. Gynecol.2014; 211:365.e1-365.e12). One of main reasons for the failure to obtaina result on NIPT is the low fetal DNA fraction in maternal plasma DNA insome samples, usually <4% (Gil et al. Fetal Diagn. Ther. 2014;35:156-73). It was demonstrated that in patients with a fetal DNAfraction below 4%, the prevalence of aneuploidy was reported to be 4.7%,which was significantly higher compared with the prevalence of 0.4% inthe overall cohort (Norton et al. N. Engl. J Med. 2015; 372:1589-1597).Therefore, such test failures can ultimately adversely affect theoverall performance of NIPT. For example, it was illustrated that thehigher test failure rate would lead to lower actual PPVs (Yaron Prenat.Diagn. 2016; 36:391-6). In a theoretical estimation (Yaron Prenat.Diagn. 2016; 36:391-6), a failure rate of 0.1% in a laboratory wouldgive an actual PPV of 67%, however a failure rate of 1% would give riseto an actual PPV of 16.7% assuming that all these patients with testfailures that were reported to be associated with an increased risk ofaneuploidy will undergo invasive testing to ascertain if the fetuses areindeed aneuploid according to recommendations from the American Congressof Obstetricians and Gynecologists (ACOG) recommendation (Yaron Prenat.Diagn. 2016; 36:391-6).

It has been shown that approximately 2% of pregnancies have a fetal DNAfraction lower than 4% (Wang et al. Prenat. Diagn. 2013; 33:662-666). Itis unlikely that the blood redraw for the patients with a first bloodsample showing a low fetal DNA fraction would warrant an sufficientfetal DNA fraction because the increase of fetal DNA between 10 and 21weeks is very subtle (with approximately a 0.1% average weekly increasein fetal DNA fraction) (Wang et al. Prenat. Diagn. 2013; 33:662-666). Inaddition, such low fetal DNA fractions preferentially occur in womenwith high maternal weights. In some studies, the failure to report aresult due to fetal DNA fraction less than 4% could be as high as 5.9%(Hall et al. PLoS One 2014; 9:e96677).

Therefore, it would be useful to develop an approach for improving theperformance of NIPT for pregnant women with low fetal DNA fractions inmaternal plasma (e.g., below 4%), Such improvements would be valuablefor the performance of NIPT for common chromosomal aneuploidies (e.g.trisomy 21, trisomy 18, trisomy 13, and sex chromosome aneuploidies) aswell as for sub-chromosomal aberrations (e.g. microdeletions andmicroduplications). In addition, improving accuracy and efficiency oftesting for copy number aberrations and cancer can be addressed withsimilar approaches. These and other needs are addressed below.

SUMMARY

Size-band analysis is used to determine whether a chromosomal regionexhibits a copy number aberration or is used to detect cancer. Multiplesize ranges may be analyzed instead of focusing on specific sizes. Byusing multiple size ranges instead of specific sizes, methods may beable to determine whether a chromosomal region exhibits a copy numberaberration even when clinically-relevant DNA may be a low fraction ofthe biological sample. Using multiple ranges may allow for the use ofall sequence reads from a genomic region, rather than a selected subsetof reads in the genomic region. The accuracy of analysis may beincreased with higher sensitivity at similar or higher specificity.Analysis may include fewer sequencing reads to achieve the sameaccuracy, resulting in a more efficient process. Because analysis may bedone with a lower fraction of clinically-relevant DNA, analysis may bedone at an earlier stage of pregnancy or cancer.

A better understanding of the nature and advantages of embodiments ofthe present invention may be gained with reference to the followingdetailed description and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic illustration of the principle of plasma DNAsize-band analysis according to embodiments of the present invention.

FIG. 2A shows the measured fetal DNA fraction for an aneuploidchromosome for sizes of plasma DNA fragment according to embodiments ofthe present invention.

FIG. 2B shows the z-score for size bands for samples including DNA fromeuploidy and trisomy 21 fetuses according to embodiments of the presentinvention.

FIG. 3 shows the size-band based changing patterns of the measuredgenomic representations (GRs) for an aneuploid chromosome acrossdifferent individual pregnancies with a fetal DNA fraction of 4%according to embodiments of the present invention.

FIG. 4A shows a heatmap plot of size-band based changing patternsbetween pregnancies with euploid and trisomy 21 fetuses according toembodiments of the present invention.

FIG. 4B shows t-SNE (t-distributed stochastic neighbor embedding) plotof size-band based changing patterns between pregnancies with euploidand trisomy 21 fetuses according to embodiments of the presentinvention.

FIG. 4C shows z-score distributions using conventional z-score approachbetween pregnancies with euploid and trisomy 21 fetuses according toembodiments of the present invention.

FIGS. 5A and 5B show performance evaluation for neural network basedmodel by learning z-score patterns among different size bands accordingto embodiments of the present invention.

FIG. 6 shows a method of determining whether a chromosomal regionexhibits a copy number aberration in a biological sample from a subjectaccording to embodiments of the present invention.

FIG. 7 shows size-band based changing patterns of the measuredmethylation in plasma DNA of hepatocellular carcinoma (HCC) patientsaccording to embodiments of the present invention.

FIG. 8 shows a method of determining a cancer classification in abiological sample from a subject according to embodiments of the presentinvention.

FIG. 9 shows size-band based changing patterns of the measured copynumber aberrations in plasma DNA of hepatocellular carcinoma (HCC)patients according to embodiments of the present invention.

FIG. 10 illustrates a workflow for a size-banded genomic representation(GR) approach for cancer detection according to embodiments of thepresent invention.

FIGS. 11A, 11B, and 11C show a comparison between size-banded GR andconventional z-score approaches according to embodiments of the presentinvention.

FIG. 12 shows a method of determining a cancer classification accordingto embodiments of the present invention.

FIG. 13 illustrates a workflow for a size-banded methylation density(MD) approach for cancer detection according to embodiments of thepresent invention.

FIGS. 14A, 14B, and 14C show a comparison between size-banded MD andconventional z-score approaches according to embodiments of the presentinvention.

FIG. 15 illustrates a system according to embodiments of the presentinvention.

FIG. 16 shows a computer system according to embodiments of the presentinvention.

TERMS

The term “sample”, “biological sample” or “patient sample” is meant toinclude any tissue or material derived from a living or dead subject. Abiological sample may be a cell-free sample, which may include a mixtureof nucleic acid molecules from the subject and potentially nucleic acidmolecules from a pathogen, e.g., a virus. A biological sample generallycomprises a nucleic acid (e.g., DNA or RNA) or a fragment thereof. Theterm “nucleic acid” may generally refer to deoxyribonucleic acid (DNA),ribonucleic acid (RNA) or any hybrid or fragment thereof. The nucleicacid in the sample may be a cell-free nucleic acid. A sample may be aliquid sample or a solid sample (e.g., a cell or tissue sample). Thebiological sample can be a bodily fluid, such as blood, plasma, serum,urine, vaginal fluid, fluid from a hydrocele (e.g., of the testis),vaginal flushing fluids, pleural fluid, ascitic fluid, cerebrospinalfluid, saliva, sweat, tears, sputum, bronchoalveolar lavage fluid,discharge fluid from the nipple, aspiration fluid from different partsof the body (e.g., thyroid, breast), etc. Stool samples can also beused. In various embodiments, the majority of DNA in a biological samplethat has been enriched for cell-free DNA (e.g., a plasma sample obtainedvia a centrifugation protocol) can be cell-free (e.g., greater than 50%,60%, 70%, 80%, 90%, 95%, or 99% of the DNA can be cell-free). Thecentrifugation protocol can include, for example, 3,000 g×10 minutes,obtaining the fluid part, and re-centrifuging at, for example, 30,000 gfor another 10 minutes to remove residual cells.

As used herein, the term “locus” or its plural form “loci” is a locationor address of any length of nucleotides (or base pairs) which has avariation across genomes. The term “sequence read” refers to a sequenceobtained from all or part of a nucleic acid molecule, e.g., a DNAfragment. In one embodiment, just one end of the fragment is sequenced.Alternatively, both ends (e.g., about 30 bp from each end) of thefragment can be sequenced to generate two sequence reads. The pairedsequence reads can then be aligned to a reference genome, which canprovide a length of the fragment. In yet another embodiment, a linearDNA fragment can be circularized, e.g., by ligation, and the partspanning the ligation site can be sequenced.

The term “fragment” (e.g., a DNA fragment), as used herein, can refer toa portion of a polynucleotide or polypeptide sequence that comprises atleast 3 consecutive nucleotides. A nucleic acid fragment can retain thebiological activity and/or some characteristics of the parentpolypeptide. A nucleic acid fragment can be double-stranded orsingle-stranded, methylated or unmethylated, intact or nicked, complexedor not complexed with other macromolecules, e.g. lipid particles,proteins. A tumor-derived nucleic acid can refer to any nucleic acidreleased from a tumor cell, including pathogen nucleic acids frompathogens in a tumor cell.

The term “assay” generally refers to a technique for determining aproperty of a nucleic acid. An assay (e.g., a first assay or a secondassay) generally refers to a technique for determining the quantity ofnucleic acids in a sample, genomic identity of nucleic acids in asample, the copy number variation of nucleic acids in a sample, themethylation status of nucleic acids in a sample, the fragment sizedistribution of nucleic acids in a sample, the mutational status ofnucleic acids in a sample, or the fragmentation pattern of nucleic acidsin a sample. Any assay known to a person having ordinary skill in theart may be used to detect any of the properties of nucleic acidsmentioned herein. Properties of nucleic acids include a sequence,quantity, genomic identity, copy number, a methylation state at one ormore nucleotide positions, a size of the nucleic acid, a mutation in thenucleic acid at one or more nucleotide positions, and the pattern offragmentation of a nucleic acid (e.g., the nucleotide position(s) atwhich a nucleic acid fragments). The term “assay” may be usedinterchangeably with the term “method”. An assay or method can have aparticular sensitivity and/or specificity, and their relative usefulnessas a diagnostic tool can be measured using ROC-AUC statistics.

The term “random sequencing,” as used herein, generally refers tosequencing whereby the nucleic acid fragments sequenced have not beenspecifically identified or predetermined before the sequencingprocedure. Sequence-specific primers to target specific gene loci arenot required. In some embodiments, adapters are added to the end of afragment, and the primers for sequencing attached to the adapters. Thus,any fragment can be sequenced with the same primer that attaches to asame universal adapter, and thus the sequencing can be random. Massivelyparallel sequencing may be performed using random sequencing.

“Nucleic acid” may refer to deoxyribonucleotides or ribonucleotides andpolymers thereof in either single- or double-stranded form. The term mayencompass nucleic acids containing known nucleotide analogs or modifiedbackbone residues or linkages, which are synthetic, naturally occurring,and non-naturally occurring, which have similar binding properties asthe reference nucleic acid, and which are metabolized in a mannersimilar to the reference nucleotides. Examples of such analogs mayinclude, without limitation, phosphorothioates, phosphoramidites, methylphosphonates, chiral-methyl phosphonates, 2-O-methyl ribonucleotides,peptide-nucleic acids (PNAs).

Unless otherwise indicated, a particular nucleic acid sequence alsoimplicitly encompasses conservatively modified variants thereof (e.g.,degenerate codon substitutions) and complementary sequences, as well asthe sequence explicitly indicated. Specifically, degenerate codonsubstitutions may be achieved by generating sequences in which the thirdposition of one or more selected (or all) codons is substituted withmixed-base and/or deoxyinosine residues (Batzer et al., Nucleic AcidRes. 19:5081 (1991); Ohtsuka et al., J. Biol. Chem. 260:2605-2608(1985); Rossolini et al., Mol. Cell. Probes 8:91-98 (1994)). The termnucleic acid is used interchangeably with gene, cDNA, mRNA,oligonucleotide, and polynucleotide.

The term “nucleotide,” in addition to referring to the naturallyoccurring ribonucleotide or deoxyribonucleotide monomers, may beunderstood to refer to related structural variants thereof, includingderivatives and analogs, that are functionally equivalent with respectto the particular context in which the nucleotide is being used (e.g.,hybridization to a complementary base), unless the context clearlyindicates otherwise.

A “sequence read” refers to a string of nucleotides sequenced from anypart or all of a nucleic acid molecule. For example, a sequence read maybe the entire nucleic acid fragment that exists in the biologicalsample. Also as an example, a sequence read may be a short string ofnucleotides (e.g., 20-150 bases) sequenced from a nucleic acid fragment,a short string of nucleotides at one or both ends of a nucleic acidfragment, or the sequencing of the entire nucleic acid fragment thatexists in the biological sample. A sequence read may be obtained in avariety of ways, e.g., using sequencing techniques or using probes,e.g., in hybridization arrays or capture probes, or amplificationtechniques, such as the polymerase chain reaction (PCR) or linearamplification using a single primer or isothermal amplification, orbased on biophysical measurements, such as mass spectrometry. A sequenceread may be obtained from a single-molecule sequencing. “Single-moleculesequencing” refers to sequencing of a single template DNA molecule toobtain a sequence read without the need to interpret base sequenceinformation from clonal copies of a template DNA molecule. Thesingle-molecule sequencing may sequence the entire molecule or only partof the DNA molecule. A majority of the DNA molecule may be sequenced,e.g., greater than 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 95%, or99%.

The term “universal sequencing” refers to sequencing where adapters areadded to the end of a fragment, and the primers for sequencing attachedto the adapters. Thus, any fragment can be sequenced with the sameprimer, and thus the sequencing can be random.

Examples of “clinically-relevant” DNA include fetal DNA in maternalplasma and tumor DNA in the patient's plasma. Another example includethe measurement of the amount of graft-associated DNA in the plasma of atransplant patient. A further example include the measurement of therelative amounts of hematopoietic and nonhematopoietic DNA in the plasmaof a subject. This latter embodiment can be used for detecting ormonitoring or prognosticating pathological processes or injuriesinvolving hematopoietic and/or nonhematopoietic tissues.

The term “level of cancer” (or more generally “level of disease” or“level of condition”) can refer to whether cancer exists (i.e., presenceor absence), a stage of a cancer, a size of tumor, whether there ismetastasis, the total tumor burden of the body, the cancer's response totreatment, and/or other measure of a severity of a cancer (e.g.recurrence of cancer). The level of cancer may be a number (e.g., aprobability) or other indicia, such as symbols, alphabet letters, andcolors. The level may be zero. The level of cancer may also includepremalignant or precancerous conditions (states). The level of cancercan be used in various ways. For example, screening can check if canceris present in someone who is not known previously to have cancer.Assessment can investigate someone who has been diagnosed with cancer tomonitor the progress of cancer over time, study the effectiveness oftherapies or to determine the prognosis. In one embodiment, theprognosis can be expressed as the chance of a patient dying of cancer,or the chance of the cancer progressing after a specific duration ortime, or the chance of cancer metastasizing. Detection can mean‘screening’ or can mean checking if someone, with suggestive features ofcancer (e.g. symptoms or other positive tests), has cancer. A “level ofpathology” can refer to level of pathology associated with a pathogen,where the level can be as described above for cancer. The level ofdiseases/condition can also be as described above for cancer. When thecancer is associated with a pathogen, a level of cancer can be a type ofa level of pathology.

The term “chromosome aneuploidy” as used herein means a variation in thequantitative amount of a chromosome from that of a diploid genome. Thevariation may be a gain or a loss. It may involve the whole of onechromosome or a region of a chromosome.

The term “sequence imbalance” or “aberration” as used herein means anysignificant deviation as defined by at least one cutoff value in aquantity of the clinically relevant chromosomal region from a referencequantity. A sequence imbalance can include chromosome dosage imbalance,allelic imbalance, mutation dosage imbalance, copy number imbalance,haplotype dosage imbalance, and other similar imbalances. As an example,an allelic imbalance can occur when a tumor has one allele of a genedeleted or one allele of a gene amplified or differential amplificationof the two alleles in its genome, thereby creating an imbalance at aparticular locus in the sample. As another example, a patient could havean inherited mutation in a tumor suppressor gene. The patient could thengo on to develop a tumor in which the non-mutated allele of the tumorsuppressor gene is deleted. Thus, within the tumor, there is mutationdosage imbalance. When the tumor releases its DNA into the plasma of thepatient, the tumor DNA will be mixed in with the constitutional DNA(from normal cells) of the patient in the plasma. Through the use ofmethods described herein, mutational dosage imbalance of this DNAmixture in the plasma can be detected. An aberration can include adeletion or amplification of a chromosomal region.

“DNA methylation” in mammalian genomes typically refers to the additionof a methyl group to the 5′ carbon of cytosine residues (i.e.5-methylcytosines) among CpG dinucleotides. DNA methylation may occur incytosines in other contexts, for example CHG and CHH, where H isadenine, cytosine or thymine. Cytosine methylation may also be in theform of 5-hydroxymethylcytosine. Non-cytosine methylation, such asN6-methyladenine, has also been reported.

A “classification” refers to any number(s) or other characters(s) thatare associated with a particular property of a sample. For example, a“+” symbol (or the word “positive”) could signify that a sample isclassified as having deletions or amplifications. The classification canbe binary (e.g., positive or negative) or have more levels ofclassification (e.g., a scale from 1 to 10 or 0 to 1).

The term “cutoff” and “threshold” can refer to a predetermined numberused in an operation. A threshold or reference value may be a valueabove or below which a particular classification applies, e.g., aclassification of a condition, such as whether a subject has a conditionor a severity of the condition. A cutoff may be predetermined with orwithout reference to the characteristics of the sample or the subject.For example, cutoffs may be chosen based on the age or sex of the testedsubject. A cutoff may be chosen after and based on output of the testdata. For example, certain cutoffs may be used when the sequencing of asample reaches a certain depth. As another example, reference subjectswith known classifications of one or more conditions and measuredcharacteristic values (e.g., a methylation level, a statistical sizevalue, or a count) can be used to determine reference levels todiscriminate between the different conditions and/or classifications ofa condition (e.g., whether the subject has the condition). Any of theseterms can be used in any of these contexts. As will be appreciated byone of skilled in the art, a cutoff can be selected to achieve a desiredsensitivity and specificity.

A “site” (also called a “genomic site”) corresponds to a single site,which may be a single base position or a group of correlated basepositions, e.g., a CpG site or larger group of correlated basepositions. A “locus” may correspond to a region that includes multiplesites. A locus can include just one site, which would make the locusequivalent to a site in that context.

The “methylation index” for each genomic site (e.g., a CpG site) canrefer to the proportion of DNA fragments (e.g., as determined fromsequence reads or probes) showing methylation at the site over the totalnumber of reads covering that site. A “read” can correspond toinformation (e.g., methylation status at a site) obtained from a DNAfragment. A read can be obtained using reagents (e.g. primers or probes)that preferentially hybridize to DNA fragments of a particularmethylation status. Typically, such reagents are applied after treatmentwith a process that differentially modifies or differentially recognizesDNA molecules depending of their methylation status, e.g. bisulfiteconversion, or methylation-sensitive restriction enzyme, or methylationbinding proteins, or anti-methylcytosine antibodies. In anotherembodiment, single molecule sequencing techniques that recognizemethylcytosines and hydroxymethylcytosines can be used for elucidatingthe methylation status and for determining a methylation index.

The “methylation density” of a region can refer to the number of readsat sites within the region showing methylation divided by the totalnumber of reads covering the sites in the region. The sites may havespecific characteristics, e.g., being CpG sites. Thus, the “CpGmethylation density” of a region can refer to the number of readsshowing CpG methylation divided by the total number of reads coveringCpG sites in the region (e.g., a particular CpG site, CpG sites within aCpG island, or a larger region). For example, the methylation densityfor each 100-kb bin in the human genome can be determined from the totalnumber of cytosines not converted after bisulfite treatment (whichcorresponds to methylated cytosine) at CpG sites as a proportion of allCpG sites covered by sequence reads mapped to the 100-kb region. Thisanalysis can also be performed for other bin sizes, e.g. 500 bp, 5 kb,10 kb, 50-kb or 1-Mb, etc. A region could be the entire genome or achromosome or part of a chromosome (e.g. a chromosomal arm). Themethylation index of a CpG site is the same as the methylation densityfor a region when the region only includes that CpG site. The“proportion of methylated cytosines” can refer to the number of cytosinesites, “C's”, that are shown to be methylated (for example unconvertedafter bisulfite conversion) over the total number of analyzed cytosineresidues, i.e. including cytosines outside of the CpG context, in theregion. The methylation index, methylation density, and proportion ofmethylated cytosines are examples of “methylation levels,” which mayinclude other ratios involving counts of methylated reads at sites.Apart from bisulfite conversion, other processes known to those skilledin the art can be used to interrogate the methylation status of DNAmolecules, including, but not limited to enzymes sensitive to themethylation status (e.g. methylation-sensitive restriction enzymes),methylation binding proteins, single molecule sequencing using aplatform sensitive to the methylation status (e.g. nanopore sequencing(Schreiber et al. Proc Natl Acad Sci 2013; 110: 18910-18915) and by thePacific Biosciences single molecule real time analysis (Flusberg et al.Nat Methods 2010; 7: 461-465)).

“Methylation-aware sequencing” refers to any sequencing method thatallows one to ascertain the methylation status of a DNA molecule duringa sequencing process, including, but not limited to bisulfitesequencing, or sequencing preceded by methylation-sensitive restrictionenzyme digestion, immunoprecipitation using anti-methylcytosine antibodyor methylation binding protein, or single molecule sequencing thatallows elucidation of the methylation status. A “methylation-awareassay” or “methylation-sensitive assay” can include both sequencing andnon-sequencing based methods, such as MSP, probe based interrogation,hybridization, restriction enzyme digestion followed by densitymeasurements, anti-methylcytosine immunoassays, mass spectrometryinterrogation of proportion of methylated cytosines orhydroxymethylcytosines, immunoprecipitation not followed by sequencing,etc.

A “separation value” (or relative abundance) corresponds to a differenceor a ratio involving two values, e.g., two amounts of DNA molecules, twofractional contributions, or two methylation levels, such as a sample(mixture) methylation level and a reference methylation level. Theseparation value could be a simple difference or ratio. As examples, adirect ratio of x/y is a separation value, as well as x/(x+y). Theseparation value can include other factors, e.g., multiplicativefactors. As other examples, a difference or ratio of functions of thevalues can be used, e.g., a difference or ratio of the naturallogarithms (ln) of the two values. A separation value can include adifference and/or a ratio. A methylation level is an example of arelative abundance, e.g., between methylated DNA molecules (e.g., atparticular sites) and other DNA molecules (e.g., all other DNA moleculesat particular sites or just unmethylated DNA molecules). The amount ofother DNA molecules can act as a normalization factor. As anotherexample, an intensity of methylated DNA molecules (e.g., fluorescent orelectrical intensity) relative to intensity of all or unmethylated DNAmolecules can be determined. The relative abundance can also include anintensity per volume.

The terms “control”, “control sample”, “reference”, “reference sample”,“normal”, and “normal sample” may be interchangeably used to generallydescribe a sample that does not have a particular condition, or isotherwise healthy. In an example, a method as disclosed herein may beperformed on a subject having a tumor, where the reference sample is asample taken from a healthy tissue of the subject. In another example,the reference sample is a sample taken from a subject with the disease,e.g. cancer or a particular stage of cancer. A reference sample may beobtained from the subject, or from a database. The reference generallyrefers to a reference genome that is used to map sequence reads obtainedfrom sequencing a sample from the subject. A reference genome generallyrefers to a haploid or diploid genome to which sequence reads from thebiological sample and the constitutional sample can be aligned andcompared. For a haploid genome, there is only one nucleotide at eachlocus. For a diploid genome, heterozygous loci can be identified, withsuch a locus having two alleles, where either allele can allow a matchfor alignment to the locus. A reference genome may correspond to avirus, e.g., by including one or more viral genomes.

The phrase “healthy,” as used herein, generally refers to a subjectpossessing good health. Such a subject demonstrates an absence of anymalignant or non-malignant disease. A “healthy individual” may haveother diseases or conditions, unrelated to the condition being assayed,that may normally not be considered “healthy”.

The terms “cancer” or “tumor” may be used interchangeably and generallyrefer to an abnormal mass of tissue wherein the growth of the masssurpasses and is not coordinated with the growth of normal tissue. Acancer or tumor may be defined as “benign” or “malignant” depending onthe following characteristics: degree of cellular differentiationincluding morphology and functionality, rate of growth, local invasion,and metastasis. A “benign” tumor is generally well differentiated, hascharacteristically slower growth than a malignant tumor, and remainslocalized to the site of origin. In addition, a benign tumor does nothave the capacity to infiltrate, invade, or metastasize to distantsites. A “malignant” tumor is generally poorly differentiated(anaplasia), has characteristically rapid growth accompanied byprogressive infiltration, invasion, and destruction of the surroundingtissue. Furthermore, a malignant tumor has the capacity to metastasizeto distant sites. “Stage” can be used to describe how advance amalignant tumor is. Early stage cancer or malignancy is associated withless tumor burden in the body, generally with less symptoms, with betterprognosis, and with better treatment outcome than a late stagemalignancy. Late or advanced stage cancer or malignancy is oftenassociated with distant metastases and/or lymphatic spread.

The term “false positive” (FP) can refer to subjects not having acondition. False positive generally refers to subjects not having atumor, a cancer, a pre-cancerous condition (e.g., a precancerouslesion), a localized or a metastasized cancer, a non-malignant disease,or are otherwise healthy. The term false positive generally refers tosubjects not having a condition, but are identified as having thecondition by an assay or method of the present disclosure.

The terms “sensitivity” or “true positive rate” (TPR) can refer to thenumber of true positives divided by the sum of the number of truepositives and false negatives. Sensitivity may characterize the abilityof an assay or method to correctly identify a proportion of thepopulation that truly has a condition. For example, sensitivity maycharacterize the ability of a method to correctly identify the number ofsubjects within a population having cancer. In another example,sensitivity may characterize the ability of a method to correctlyidentify one or more markers indicative of cancer.

The terms “specificity” or “true negative rate” (TNR) can refer to thenumber of true negatives divided by the sum of the number of truenegatives and false positives. Specificity may characterize the abilityof an assay or method to correctly identify a proportion of thepopulation that truly does not have a condition. For example,specificity may characterize the ability of a method to correctlyidentify the number of subjects within a population not having cancer.In another example, specificity may characterize the ability of a methodto correctly identify one or more markers indicative of cancer.

The term “ROC” or “ROC curve” can refer to the receiver operatorcharacteristic curve. The ROC curve can be a graphical representation ofthe performance of a binary classifier system. For any given method, anROC curve may be generated by plotting the sensitivity against thespecificity at various threshold settings. The sensitivity andspecificity of a method for detecting the presence of a tumor in asubject may be determined at various concentrations of tumor-derivednucleic acid in the plasma sample of the subject. Furthermore, providedat least one of the three parameters (e.g., sensitivity, specificity,and the threshold setting), and ROC curve may determine the value orexpected value for any unknown parameter. The unknown parameter may bedetermined using a curve fitted to the ROC curve. The term “AUC” or“ROC-AUC” generally refers to the area under a receiver operatorcharacteristic curve. This metric can provide a measure of diagnosticutility of a method, taking into account both the sensitivity andspecificity of the method. Generally, ROC-AUC ranges from 0.5 to 1.0,where a value closer to 0.5 indicates the method has limited diagnosticutility (e.g., lower sensitivity and/or specificity) and a value closerto 1.0 indicates the method has greater diagnostic utility (e.g., highersensitivity and/or specificity). See, e.g., Pepe et al, “Limitations ofthe Odds Ratio in Gauging the Performance of a Diagnostic, Prognostic,or Screening Marker,” Am. J. Epidemiol 2004, 159 (9): 882-890, which isentirely incorporated herein by reference. Additional approaches forcharacterizing diagnostic utility using likelihood functions, oddsratios, information theory, predictive values, calibration (includinggoodness-of-fit), and reclassification measurements are summarizedaccording to Cook, “Use and Misuse of the Receiver OperatingCharacteristic Curve in Risk Prediction,” Circulation 2007, 115:928-935, which is entirely incorporated herein by reference.

The term “about” or “approximately” can mean within an acceptable errorrange for the particular value as determined by one of ordinary skill inthe art, which will depend in part on how the value is measured ordetermined, i.e., the limitations of the measurement system. Forexample, “about” can mean within 1 or more than 1 standard deviation,per the practice in the art. Alternatively, “about” can mean a range ofup to 20%, up to 10%, up to 5%, or up to 1% of a given value.Alternatively, particularly with respect to biological systems orprocesses, the term “about” or “approximately” can mean within an orderof magnitude, within 5-fold, and more preferably within 2-fold, of avalue. Where particular values are described in the application andclaims, unless otherwise stated the term “about” meaning within anacceptable error range for the particular value should be assumed. Theterm “about” can have the meaning as commonly understood by one ofordinary skill in the art. The term “about” can refer to ±10%. The term“about” can refer to ±5%.

The terminology used herein is for the purpose of describing particularcases only and is not intended to be limiting. As used herein, thesingular forms “a”, “an” and “the” are intended to include the pluralforms as well, unless the context clearly indicates otherwise. The useof “or” is intended to mean an “inclusive or,” and not an “exclusive or”unless specifically indicated to the contrary. The term “based on” isintended to mean “based at least in part on.” Furthermore, to the extentthat the terms “including”, “includes”, “having”, “has”, “with”, orvariants thereof are used in either the detailed description and/or theclaims, such terms are intended to be inclusive in a manner similar tothe term “comprising.”

DETAILED DESCRIPTION

Size-based analysis of cell-free DNA has been used in analyzingbiological samples for chromosomal aneuploidies and cancer. However,with previous size-based techniques, when the biological sample has alow percentage of clinically-relevant DNA, obtaining a statisticallysignificant result may be difficult. When the fraction ofclinically-relevant DNA is low, previous size-based analysis may be usedto confirm the results of another type of analysis rather than reliedupon as a single analysis technique. Embodiments of the presentinvention involve using size bands, which may allow for more cell-freeDNA to be used in analysis and may allow for patterns of sizes to beanalyzed. As a result, size-based analysis may be performed accuratelyat even low fractions of clinically-relevant DNA.

In this study, we aimed to apply size analysis of cell-free DNA to lowerthe limit of fetal DNA fraction required for NIPT. We aim to improve thesensitivity of NIPT, without adversely impacting the specificity.Similar techniques may be applied to cancer analysis. Using multiplesize ranges instead of specific sizes was found to allow for analysis ofbiological samples even when the fraction of clinically-relevant DNA islow. Embodiments may include using size bands to determine whether achromosomal region exhibits a copy number aberration (CNA). The CNA maybe related to an aneuploidy or cancer. Embodiments may also includeusing size bands to determine a level of cancer.

I. Size-Based Analysis

It has been demonstrated that the fetal-derived molecules in maternalplasma are shorter than the maternal DNA molecules (Chan et al. ClinChem 2004; 50:88-92; Lo et al. Sci. Transl. Med. 2010; 2:61ra91-61ra91).Researchers have made use of such a size difference to enrich for fetalDNA in maternal plasma samples for NIPT (Li et al. Clin Chem 2004;50:1002-1011, JAMA 2005; 293:843-9; Lun et al. Proc. Natl. Acad. Sci.U.S.A. 2008; 105:19920-5). Yu et al. had illustrated that fetalchromosomal aneuploidies could be detected by determining an aberrantproportion of short fragments from an aneuploid chromosome in paired-endsequencing data (Yu et al. Proc. Natl. Acad. Sci. U.S.A. 2014;111:8583-8). Such an approach can achieve good NIPT performance whencompared with the counting of DNA molecules in maternal plasma (Yu etal. Proc. Natl. Acad. Sci. U.S.A. 2014; 111:8583-8).

To improve the accuracy of noninvasive detection of fetal chromosomalabnormalities in pregnant women with low fetal DNA fractions (e.g. <4%),one possible method that has been previously explored is the selectiveanalysis of short DNA molecules through in silico size selection orphysical size selection (e.g., WO 2009/013496, filed Jul. 23, 2008,which is incorporated herein by reference for all purposes). In thesemethods, data or molecules from the short plasma DNA molecules form thebasis for statistical analyses, disease classification, and caseinterpretation. As fetal-derived DNA molecules have a shorter sizedistribution compared with maternal-derived ones, the selective analysisof short DNA fragments could preferentially enrich fetal-derived DNAmolecules, resulting in higher fetal DNA fractions.

As fetal DNA fraction is a key factor governing the NIPT performance,this may potentially improve the accuracy of NIPT. However, it wasreported that in-silico selection of sequenced reads with lengths <150bp could increase the effective fetal DNA fraction but would notnecessarily increase the sensitivity of aneuploidy detection bysingle-molecule counting because of a trade-off between the fetal DNAfraction and the number of molecules being counted (Fan et al. Clin.Chem. 2010; 56:1279-1286). In other words, as shown in Table 1, theprevious approaches with selecting short DNA could not improve thesensitivity without increasing sequencing depth because of the markedreduction in number of plasma DNA fragments that are counted. Reducingthe size of the plasma DNA fragments analyzed reduces the number of DNAfragments that are analyzed. For example, if only lengths less than 100bp are analyzed, the DNA fragments undergo a 48.5 fold reduction. At thesame time, by focusing on smaller plasma DNA fragments, the fetal DNAfraction is enriched. For example, for lengths less than 100 bp, thefetal DNA fraction has a 1.78 fold enrichment. However, the 1.78 foldenrichment is small compared to the 48.5 fold reduction in plasma DNAmolecules being analyzed.

TABLE 1 The fold reduction The fold enrichment in plasma DNA Plasma DNAin fetal DNA molecules being size (bp) fraction (x) analyzed (x) <1501.93 4.67 <120 2.04 21.2 <110 1.91 32.3 <100 1.78 48.5

On the other hand, we have previously developed another plasma DNAsize-based approach (U.S. Pat. No. 8,620,593) to improve diagnosticspecificity by taking advantage of DNA molecules below a certainthreshold, for example 150 bp in size. In this method, average size ofplasma DNA molecules derived from a potential aneuploidy chromosome arecompared with the average size of plasma DNA molecules derived fromother chromosomes. This approach has been shown to improve thespecificity of non-invasive detection of chromosomal aneuploidiesbecause fetal chromosomal aneuploidies would result in shortening of theaverage size of the plasma DNA molecules from an overrepresentedchromosome (e.g. trisomic chromosome) or lengthening of the average sizeof plasma DNA molecules for an underrepresented chromosome (e.g.monosomic chromosome). However, such an approach could not be expectedto enhance the sensitivity because of the reduction in number of plasmaDNA molecules counted.

There were some previous efforts attempting to use the in silicoselection of particular short DNA molecules to quantify the copy numberchanges of an aneuploid chromosome (Fan et al. Clin. Chem. 2010;56:1279-1286). However, such a specific size selection would reduce thenumber of DNA molecules that would contribute to the final clinicalclassification, therefore increasing the stochastic variations.Analytically, such increase in stochastic variations may be manifestedas increase in the coefficient of variation (CV) or standard deviation(SD). According to the Poisson distribution, for every 4-fold reductionin the number of molecules being analyzed, the CV would increase 2-fold.On the other hand, for every 2-fold increase in the fractionalconcentration of circulating fetal DNA, the number of molecules that onewould need to count to arrive at a correct diagnosis of fetalchromosomal aneuploidy would decrease by 4-fold. If one would use thesize selection for those molecules below 150 bp, the fetal DNA fractionwould increase ˜2-fold but the number of plasma DNA molecules would bedecreased 4.7-fold. Therefore, the enrichment in fetal DNA fractionsthrough a simple size selection would not be able to effectively offsetthe detrimental effect of the reduction of plasma DNA molecules, whichmight be an important reason why there was no consistent improvement inNIPT by a simple in silico size selection (Fan et al. Clin. Chem. 2010;56:1279-1286).

II. Size Patterns

In this study, we developed a new way to incorporate the plasma DNA sizeinformation by making use of the detailed changing patterns of moleculecounts across a series of different size ranges, which according to theempirical data has surprisingly resulted in an improvement in the testsensitivity. It is counter-intuitive because when fractionating plasmaDNA molecules into more size bands, there should be far fewer sequencedDNA molecules per size band, and plasma DNA molecules within each bandalone were not able to improve sensitivity. Instead of using oneparticular band alone, our new approach is to use the relationshipacross different bands to improve the performance.

We reasoned that the changes of genomic representation (GR) of ananeuploid chromosome would be varied in accordance with the measuredfetal DNA fractions present in different sizes of plasma DNA molecules.We hypothesized that the relationship between the GR changes of anaffected chromosome would be linked to different size ranges (sizebands) in a non-random way because the cell-free fetal and maternal DNAsizes reflect two distinct fragmentation patterns (Lo et al. Sci.Transl. Med. 2010; 2:61ra91-61ra91). Therefore, we developed a newapproach to analyze the detailed changing shapes of GR valuesoriginating from an aberrant chromosome among the different size bands.The schematic principle of this approach is illustrated in FIG. 1.

FIG. 1 shows a schematic illustration 100 of the principle of plasma DNAsize-band analysis. Maternal plasma comprises a mixture of fetal DNAmolecules (wavy red lines in section 104 and molecule 106) and maternalDNA molecules (wavy black lines in section 108 and molecule 110)originating from fetal and maternal cells, respectively. The fetal DNAmolecules are generally shorter than the maternal ones as evidenced bythe fetal DNA size profile shifting toward the left relative to that ofmaternal DNA molecules. Therefore, the measured fetal DNA fraction wouldbe changed according to different size bands, generally enriching in theshorter size ranges. Thus, for a woman pregnant with a trisomic fetus,the measured genomic representations (GRs), whose deviation fromreference group can be measured by z-score, would be expected to varyaccording to different size bands, but in contrast, no specific changeswould occur in a pregnancy with a euploid fetus.

FIG. 1 shows the size bands both as discrete bands and as slidingwindows. In the graph of frequency versus size, the different coloredcolumns (e.g., column 112) show the size bands as corresponding todiscrete size ranges. In graphs 116 and 118 of z-score (chr21) versussize, the colored columns (e.g., column 122 and column 124) show thez-scores for the different size bands. Lines 126 and 128 in graphs ofz-score versus size show results for size bands as sliding windows. Inthe pregnancy with an aneuploid fetus, line 128 indicates the z-scorefor a size band centered on a particular size. For example, a data pointwith a given x-coordinate and y-coordinate on the line 128 has a z-scoreindicated by the y-coordinate for a range of sizes centered around thesize indicated by the x-coordinate. Each z-score is a pooled z-scorecalculated for the entire size band. Hence, in graph 116 of thepregnancy with a euploid fetus, line 126 shows the results for sizebands as sliding windows. In graph 118 of the pregnancy with ananeuploid fetus, line 128 shows the results for size bands as slidingwindows.

Regardless of whether the size band is based on discrete or slidingwindows, the shape or pattern of the z-scores of the size bands isdistinctly different between a pregnancy with a euploid fetus and apregnancy with an aneuploid fetus. For example, as shown in graph 116and graph 118, the pregnancy with an aneuploid fetus shows a bimodalpattern compared to the more cyclical pattern in the pregnancy with theeuploid fetus.

The patterns of counts across the different size bands can be related tofetal DNA fraction, tumor DNA fraction, or other clinically-relevant DNAfraction. Thus, this new approach that concurrently quantifies a seriesof molecule counts across different size bands and the relationshipbetween different size-band based readouts would not lose plasma DNAmolecules when integrating plasma DNA size properties compared to anapproach that uses only specific sizes of DNA molecules. Such concurrentquantifications would improve accuracy compared with the use of justsingle readout below a certain size cutoff. The size-band patterns ofcopy number changes in plasma can be recognized with the use of, but notlimited to, machine learning approaches such as an artificial neuralnetwork, k-nearest neighbors algorithm, support vector machine, andmixture Gaussian model, etc.

A. Verifying Size Pattern Data Analysis

The size pattern (i.e., the shape of a fraction or a parameter relatedto the amount of cell-free DNA at a particular size band) may depend oncharacteristics of the cell-free DNA. For example, the size pattern maydepend on whether the biological sample includes cell-free DNA from ananeuploid fetus, as in graphs 116 and 118 in FIG. 1. First, the fetalDNA fraction for different sizes of DNA is analyzed to show that certainsizes of cell-free DNA are enriched for fetal DNA compared to maternalDNA. Second, data from a pregnant female with an aneuploid fetus isanalyzed using size bands against data from pregnant females witheuploid fetuses. These analyses confirm that size patterns can beanalyzed to distinguish differences in CNAs, including when the CNAs area result of an aneuploid fetus.

1. Measured Fetal DNA Fractions Vary According to Different Size Bands

To verify the hypothesis that the fetal DNA fraction changes would varyaccording to fragment sizes in a non-random manner, we reanalyzed thedata described in our previous study (Chan et al. Proc. Natl. Acad. Sci.2016; 113:E8159-E8168).

FIG. 2A shows the measured fetal DNA fraction for an aneuploidchromosome for sizes of plasma DNA fragment, ranging from 50 to 400 bp.The x-axis is the size of a DNA molecule, and the y-axis is the fractionof DNA molecules at that size that are fetal DNA. For example, at a sizeof 120 bp, the fetal DNA fraction is 70.5%, which means that of the DNAmolecules that have a size of 120 bp, 70.5% are from the fetus and 29.5%of them are from pregnant female. The fetal DNA fraction was determinedfrom the chromosome Y percentage for a sample from a pregnant femalewith a male fetus. The fetal DNA fraction was found to be enriched atthe sizes of 120 bp and 280 bp, respectively. A maximum of fetal DNAfraction of 70.5% was found at a size of 120 bp, which is 4× higher thanthe lowest one at 200 bp size with a fetal DNA fraction of 17.4%.

2. CNAs in Plasma DNA Vary for Different Size Bands

The changes in fetal DNA fractions exhibiting uneven patterns wouldimpact the presentation of molecular counts originating from ananeuploid chromosome. An aneuploid chromosome has an abnormal number ofchromosomes. An abnormal number of chromosomes in the fetus would affectthe amount of fetal DNA compared to maternal DNA. For example, trisomy21 has three chromosome 21s instead of only two. If the fetus hastrisomy 21, then fetal DNA have a higher fraction than with a normaleuploid fetus. As fetal DNA is often shorter than maternal DNA, amaternal sample of a female pregnant with a fetus with trisomy 21 wouldlikely have a higher concentration of short DNA from chromosome 21 thancompared to a maternal sample of a female pregnant with a euploid fetus.

FIG. 2B shows z-score results using size band sliding windows for apregnancy with a trisomy 21 fetus and for pregnancies with euploidfetuses. The bandwidth of the size band sliding windows was 50 bp. Thepregnancy with a trisomy 21 fetus had a fetal DNA fraction of 4%. Asseen in FIG. 2B, the 120-bp position for the trisomy 21 fetus had thehighest z-score out of all samples analyzed and therefore correspondedto the highest degree of measured copy number aberrations. Differentsize bands would affect magnitude of the z-score at 120 bp and othersizes. The calculation of the z-score of the affected chromosome isdescribed below.

Assuming that the mid-point of a size band with a 50-bp bandwidth islocated at length i (e.g. the mid-point of a size band located at an iof 75 bp and the band would range from 50 to 100 bp), then thepercentage of sequencing reads mapping to the targeted chromosome (e.g.chromosome 21) can be calculated using such fragments within aparticular size range of interest (e.g. from 50 to 100 bp), denoted as agenomic representation i (i.e. GR). The z-score for length i iscalculated:

${Z - {score}_{i}} = \frac{{GR}_{i} - M_{i}}{{SD}_{i}}$

where M_(i) and SD_(i) represent the mean and standard derivation ofgenomic representation of the targeted chromosome for the size bandcentered at length i, which was inferred in this study from 50pregnancies carrying euploid fetuses. The full spectrum of sizes will beinterrogated by dynamically changing the location of the mid-point of asize band in the size profile, ranging from 50 to 400 bp.

In FIG. 2B, we can observe regular wave-like patterns in the size-bandbased z-score curve 202 for a pregnancy with a trisomy 21 fetus. Thisobservation was reminiscent of the changes of fetal DNA fractions indifferent size bands. However, there were no such patterns shown in thecontrol group with euploid fetuses. The magnitude of such changes in aparticular size band appeared to be different from the changes of thefetal DNA fractions. For example the z-score at 120 bp was much higherthan that at 280 bp (FIG. 2B), but fetal DNA fractions were comparablebetween these two sizes (FIG. 2A). The variability may be a result ofthe molecular counts decreasing more rapidly at lengths longer than 166bp compared with lengths shorter than 166 bp so that a high samplingvariation would be present in long molecules.

FIG. 2B also shows the z-score for all sizes, illustrated as circlescorresponding to the value labeled “All” on the x-axis. Red circle 204,which is the highest circle, corresponds to trisomy 21. Red circle 204has a z-score below 3. Thus, if one would use all fragments and employ az-score of 3 as a cutoff, this case would mistakenly be classified as aeuploid fetus, resulting a false negative result. In contrast, if onewould use the distinct shape of changes in z-scores varying against thedifferent size bands, the case can be correctly identified as a trisomy21 case in comparison with the control group.

B. Applying Size Pattern Analysis

Size pattern data were generated for females pregnant with either aeuploid fetus or an aneuploid fetus. The data were then analyzed bydifferent techniques, including using machine learning models, todetermine if the size patterns could be used to distinguish betweenpregnancies with euploid fetuses and pregnancies with aneuploid fetuses.

1. Size-Band Shape of CNAs in Plasma Informs Chromosomal Aneuploidieswith Low Fetal Fraction

To evaluate whether such size-band based z-score patterns can begeneralized to other samples with low fetal DNA fractions, we analyzedan additional 111 maternal plasma DNA samples each with a male fetus,including 48 cases each with a trisomy 21 fetus and 63 cases each with aeuploid fetus. The fetal DNA fractions were estimated using Ychromosomal sequences derived from the male fetuses (Hudecova et al.PLoS One 2014; 9:e88484; Chiu et al. BMJ 2011; 342:c7401). To haveenough cases with a low fetal DNA fraction of 4% or below, eachpaired-end sequencing dataset for 48 pregnancies with trisomic fetuseswere mixed in silico with the sequencing dataset from cases with euploidfetuses to achieve the levels of 4% fetal DNA fraction or below.

FIG. 3 shows the size-band based changing patterns of the measuredgenomic representations (GRs) for an aneuploid chromosome acrossdifferent individual pregnancies with a fetal DNA fraction of 4%. Y-axisindicated z-score values, suggesting the degree of derivation formeasured GR in women pregnant with aneuploid fetuses compared with thosewith euploid fetuses. X-axis indicated different size bands. Red lines(also the darker lines) represented pregnancies with trisomic fetuses;gray lines represented those with euploid fetuses.

FIG. 3 shows that almost all of the cases with trisomic fetusesdisplayed consistently different size-band based patterns of themeasured copy number aberrations compared with those from cases witheuploid fetuses. In each case, the line for the size patterns of thetrisomy 21 case are distinctly different from the patterns for theeuploidy cases, which can allow trisomy 21 to be determined more readilythan using the z-score for all size fragments, as shown in FIG. 2B.

We further used heatmap and t-SNE (t-distributed stochastic neighborembedding) approaches to visualize the data structures betweenpregnancies carrying trisomic and euploid cases. FIG. 4A shows a heatmapplot of size-band based changing patterns between pregnancies witheuploid and trisomy 21 fetuses. Blue (e.g., area 402) is for a featureof a size band that indicates a euploid, while green (e.g., area 404) isfor a feature of a size band that indicates trisomy 21. Almost all cases(46/48, 96%) in FIG. 4A involve clustering together trisomy 21 fetuscases. Similarly, almost all cases (62/63, 98%) in FIG. 4A involving aeuploid fetus were clustered together.

FIG. 4B shows a t-SNE plot of size-band based changing patterns betweenpregnancies with euploid and trisomy 21 fetuses. The t-SNE plots arebased on two features determined from machine learning. The t-SNE plotsgave a consistent result that pregnancies with trisomy 21 cases can bereadily differentiated from those with euploid cases (FIG. 4B),suggesting the size-band based shape of measured copy number aberrationsin plasma DNA could inform chromosomal aneuploidies for cases with a lowfetal DNA fraction such as 4%.

FIG. 4C shows z-score distributions using a conventional z-scoreapproach between pregnancies with euploid and trisomy 21 fetuses. Thedashed line indicates the z-score threshold of 3. Using a z-score cutoffof 3, the detection rate of trisomy 21 would only be 48%. In otherwords, 52% of the trisomy 21 would result in a false negative. Inaddition, FIG. 4C shows that one euploidy pregnancy would result in afalse positive for trisomy 21. The conventional z-score approach wouldresult in lower sensitivity and specificity compared to the t-SNEapproach in FIG. 4B, which did not generate any false positives or falsenegatives.

2. Machine Learning Pattern Recognition for Detecting Cases with LowFetal DNA Fractions.

We utilized a neural network model to further demonstrate the use of asize-band based approach for detecting fetal copy number aberrations. Wedivided the samples into training and testing dataset. The trainingdataset included 33 pregnancies with trisomy 21 fetuses and 63 caseswith euploid fetuses, and the testing dataset contained 15 trisomy 21fetuses and 50 euploid fetuses. A neural network constructed with onelayer each with 20 neurons was used to learn a model capturing patternshidden in the size bands. Afterward, we applied this model to thetesting dataset.

FIG. 5 shows the training dataset and the testing data set for theneural network model. It turned out that with a cutoff of 0.7 for theprobability of trisomy 21, we were able to achieve 40%, 80%, 100%, and100% sensitivities at a specificity of 98% for a fetal DNA fraction of1%, 2%, 3% and 4%, respectively. Even at a low fetal DNA fraction of 1%,the neural network model shows the ability to identify true positivesfor trisomy 21.

Machine learning models other than a neural network model may be used todetermine patterns and features that can determine a probability of afetal aneuploidy or cancer in a subject. Training of these machinelearning models can use datasets including samples from those affectedby a disorder or a clinically-relevant feature and those that are not.Parameters that may be considered for training include bandwidth of thesize band, center point of the size band, amounts of DNA molecules,locations of the DNA molecules, epigenomic signals (e.g., methylation),and other variables.

3. Example Method for Detecting a Copy Number Aberration

FIG. 6 shows a method 600 of determining whether a chromosomal regionexhibits a copy number aberration in a biological sample from a subject.The biological sample may include a mixture of cell-free DNA moleculesincluding clinically-relevant DNA molecules and other DNA molecules. Theclinically-relevant DNA molecules may include fetal DNA or maternal DNA.If the clinically-relevant DNA molecules include fetal DNA, then theother DNA may include maternal DNA. If the clinically-relevant DNAmolecules include maternal DNA, then the other DNA may include fetalDNA. The clinically-relevant DNA may include tumor DNA, with the otherDNA molecules including non-tumor DNA.

At block 602, method 600 may include measuring a first amount ofcell-free DNA molecules from the biological sample corresponding to thesize range for each size range of a plurality of size ranges. Thecell-free DNA molecules may be from a particular genomic region, whichmay be a chromosome or a portion of a chromosome. For example, thegenomic region may be a chromosomal arm. The genomic region may be anyregion from the genome. In some embodiments, the cell-free DNA moleculesmay be from multiple disjoint or a continuous genomic region. A sizerange may be a size band described herein.

The particular size ranges to use may be determined by a machinelearning model. Machine learning models can be trained on datasets, andthe models can vary which ranges are used (e.g., center point positionsand/or the bandwidth of a size range) in order to optimize thesensitivity and specificity for detecting a copy number aberration or aclinical condition. The datasets may include a plurality of referencesize patterns. The machine learning model may determine that a certainbandwidth of the size range is advantageous. In addition, the machinelearning model may determine that certain size ranges may be moreimportant for a predictive result than others. For example, the sizeranges may be determined to be sliding size ranges centered around anysize from 100 bp to 150 bp. In other embodiments, the machine learningmodel may determine that discrete, non-overlapping size ranges mayprovide improved results over sliding size ranges. A cost functionrelating to a sensitivity and/or specificity or other accuracy on thetraining set can be used to update parameters and feature selection(e.g., size ranges to use and specific size ratios) for the machinelearning model. A validation data set can also be used to confirmaccuracy of the model.

At block 604, method 600 may include calculating for each size range ofthe plurality of size ranges, by a computer system, a size ratio usingthe first amount of cell-free DNA molecules corresponding to the sizerange and a second amount of DNA molecules in a second size range thatincludes sizes not in the size range. The size ratio may be a z-score ora normalized amount of cell-free DNA molecules (e.g., a fraction, apercentage, or a relative abundance). For example, the size ratio may bea genomic representation (GR). In other embodiments, the size ratio maybe a z-score calculated with GR (e.g., the z-score value at a point oncurve 202 in FIG. 2B).

Each size range may have a bandwidth, which describes the numericalvalue of the range of sizes in the size range. For example, thebandwidth may be in a range from 50 bp to 100 bp, 100 bp to 200 bp, 200bp to 300 bp, or 300 bp to 400 bp. A size range with a bandwidth of 50bp centered at 100 bp would span from 75 bp to 125 bp. Each size rangemay be non-overlapping with any other size range of the plurality ofsize ranges (e.g., discrete size bands such as column 122 and column 124in FIG. 1). In other embodiments, each size range may overlap with atleast one other size range of the plurality of size ranges. In thismanner, the size ranges may be considered sliding windows. The slidingwindows then result in size ratios values that are continuous over manysizes (e.g., line 126 or line 128 in FIG. 1).

The second size range may be larger than each size range of theplurality of size ranges. The second size range may include all sizes ofthe cell-free DNA molecules or may include all sizes of the cell-freeDNA molecules in the genomic region for the measured cell-free DNAmolecules. The second size range may include cell-free DNA moleculesfrom the same genomic regions (e.g., the same chromosome(s) orchromosomal arm(s)) as for the measured cell-free DNA molecules in block602. The second size range may also include cell-free DNA molecules fromgenomic regions other than the genomic region for the measured cell-freeDNA molecules in block 602. For example, with trisomy 21, cell-freemolecules measured at block 602 may be from chromosome 21. In this case,the second size range may include cell-free DNA molecules from otherchromosomes (e.g., a different chromosome that serves as a reference oracross the entire genome). Method 600 may then also include measuringamounts of cell-free DNA molecules that are in the second size range.

At block 606, method 600 may include obtaining a reference size patternincluding a plurality of reference size ratios for the plurality of sizeranges. The reference size pattern may be determined from a plurality ofreference samples from subjects with a copy number aberration or fromsubjects without a copy number aberration in the chromosomal region. Forexample, if the copy number aberration being tested for is related to afetal aneuploidy, the reference samples may be from subjects known tohave a euploid fetus. In other embodiments, the reference samples may befrom subjects that are known to have the fetal aneuploidy. Eachreference size ratios for the plurality of size ranges may be determinedin the same way as the size ratio calculated in block 604, except for areference sample instead of the biological sample. For example, in FIG.2B, a size pattern for a reference sample may be any one of the curvesin FIG. 2B except for curve 202. The reference size pattern may be astatistical representation of all the size patterns for the referencesamples. For example, the reference size pattern may be an average(mean, median, or mode) of all the size patterns. For example, thisaveraged reference size pattern may be line 126 in FIG. 1.

At block 608, method 600 may include comparing a plurality of the sizeratios to the reference size pattern. Comparing the plurality of sizeratios to the reference size pattern may include comparing each sizeratio of the plurality of size ratios to the reference size ratio at thecorresponding size range. For example, the plurality of size ratios maybe the points that make up line 128 in FIG. 1. In some cases, theplurality of size ratios may make up only a portion of line 128.Assuming the reference size pattern is line 126 in FIG. 1, comparing theplurality of size ratios to the reference size pattern may include astatistical comparison between the points of line 128 and the referencepoints of line 126.

Each size ratio for each size range may be determined to bestatistically similar to the reference size ratio at the correspondingsize range. Statistical similarity may be determined using a threshold.The threshold may indicate how close the size ratio needs to be to thereference size ratio. The threshold may be a certain number of standarddeviations (e.g., 1, 2, or 3) from the reference size ratio. In someembodiments, not every size ratio needs to be statistically similar tothe reference size ratio. Instead, a minimal number of size ratios maybe statistically similar. For example, 80%, 85%, 90%, or 95% of the sizeratios may be statistically similar to the corresponding reference sizeratio.

Comparing the plurality of the size ratios to the reference size patternmay include comparing the plurality of the size ratios to a plurality ofthreshold values that are determined from the plurality of referencesamples. For example, each size range may have a different thresholdvalue, which may be based on a standard deviation for reference samples.A single size range may also have different threshold values, with eachthreshold value associated with a different certainty level that thesize ratio is different from the reference samples. Comparing mayinclude counting the number of threshold values exceeded and determiningif the number exceeds an amount or fraction (e.g., 0.5, 0.6, 0.7, 0.8,or 0.9). If the number exceeds the amount, then a copy number aberrationmay be determined to be exhibited by the chromosomal region.

In some embodiments, comparing the plurality of the size ratios to thereference size pattern may include determining a size pattern includingthe plurality of size ratios for the plurality of size ranges. The sizepattern may be a graph relating the size ratios to size ranges. Forexample, the size pattern may be line 128 in FIG. 1, curve 202 in FIG.2B, or any of the Trisomy 21 lines in FIG. 3. The size pattern may bedetermined to have a similar shape as the reference size pattern.Determining a similar shape may include determining that the slopes(e.g., first derivatives) and/or the inflection points (e.g., secondderivatives) of the size pattern are similar to those in the referencesize pattern. The similarity of the slopes or inflection points may bedetermined using a threshold, which may indicate a statisticalsignificance (e.g., a certain number of standard deviations).

In some embodiments, comparing the plurality of the size ratios to thereference size pattern may include a comparison using machine learning,including a neural network. A machine learning model can be used todetermine how to calculate the size ratio, how to compare the size ratioto the reference size pattern, and/or how to determine if a size patternis similar to the reference size pattern. How to calculate the sizeratio may include determining the bandwidth of the size range and thesize and bandwidth of the second size range. How to compare the sizeratio to the reference size pattern may include determining weightingsfor different size ranges, and whether to use zeroth, first, or secondderivatives of the size pattern. How to determine if a size pattern issimilar to the reference pattern may include determining thresholdvalues for similarity.

Obtaining the reference size pattern and comparing the plurality of thesize ratios to the reference size pattern may include inputting theplurality of the size ratios to a machine learning model. The machinelearning model may be trained using a plurality of training sizepatterns from the plurality of reference samples. The trained machinelearning model (e.g., a neural network) may output a probability of asample having an aberration in a chromosomal region.

At block 610, method 600 may include determining whether the chromosomalregion exhibits a copy number aberration based on the comparison. Thecopy number aberration may be an aneuploidy, including trisomy 21,trisomy 18, trisomy 13, and sex chromosome aneuploidies. The copy numberaberration may be an indication of cancer. Method 600 may also includetreating the subject for cancer or developing a plan for an aneuploidy.

If the reference size pattern is determined from the plurality ofreference samples from subjects with a copy number aberration and thecomparison shows that the size ratios or the size pattern are similar tothe reference size pattern, then the chromosomal region may bedetermined to exhibit a copy number aberration. And if the comparisonshows differences between the size ratios or the size pattern and thereference size pattern, then the chromosomal region may be determined tonot exhibit a copy number aberration. In some embodiments, a probabilityof exhibiting the copy number aberration may be determined. Theprobability may be correlated with how similar or dissimilar the sizeratios or the size pattern is to the reference size pattern. Theprobability may be determined using a machine learning model, includinga neural network or any model described herein.

Alternatively, if the reference size pattern is determined from theplurality of reference samples from subjects without a copy numberaberration and the comparison shows that the size ratios or the sizepattern are similar to the reference size pattern, then the chromosomalregion may be determined to not exhibit a copy number aberration. And ifthe comparison shows differences between the size ratios or the sizepattern and the reference size pattern, then the chromosomal region maybe determined to exhibit a copy number aberration.

C. Improved Accuracy at Low Fetal Fractions

To benchmark the performance of approach by taking advantage ofsize-band based patterns of measured copy number aberrations in plasmaDNA, we also calculated the specificities and sensitivities acrossdifferent fetal DNA fractions such as 4%, 3%, 2%, and 1% using thetraditional z-score (Chiu et al. Proc Natl Acad Sci USA 2008;105:20458-20463) and size selection methods. Since the fetal DNA gave amaximum of measured fetal DNA fraction present in maternal plasma DNA at120 bp (FIG. 2A), we hypothesized that the size band around 120 bp wouldgive a better performance than using all DNA fragments. To this end, weselected a size band from 105 to 155 bp and calculated the correspondingz-scores.

Table 2 shows the performance of size-band based pattern recognitioncompared with the conventional counting-based methods with and without asize selection. The use of size-band based patterns of measured copynumber aberrations in plasma DNA gave a superior performance incomparison with the traditional z-score and size selection approaches.For example, in our study, at the fetal DNA fraction of 3%, therecognition of size-band based patterns of measured copy numberaberrations gave a 100% sensitivity with a specificity of 98%. Ascomparison, conventional counting based approach only gave a sensitivityof 10% and specificity of 98%. Using size selection of fragments below150 bp, the sensitivity improved to 43%. However, selection of fragmentsof even shorter size to 120 bp, the sensitivity reduced to 20%. Thisindicates that the method proposed in this invention provides muchbetter analytical performance over existing approaches using sizeselection.

TABLE 2 Size-band based patterns of measured Conventional counting-basedapproach copy number Fetal With a size selection With a size selectionWithout a size aberrations (new DNA (<120 bp) (<150 bp) selectioninvented approach) fraction Specificity Sensitivity SpecificitySensitivity Specificity Sensitivity Specificity Sensitivity 4% 96% 47%100% 75% 98% 48% 98% 100% 3% 96% 20% 100% 43% 98% 10% 98% 100% 2% 96%16% 100% 14% 98%  2% 98%  80% 1% 96%  6% 100%  6% 98%  2% 98%  40%

In addition to increased accuracy, embodiments of the present inventionmay allow for a reduced amount of sequencing. Size pattern approachesmay not involve discarding sequence reads of certain sizes, and as aresult, more sequence reads at a given sequencing depth are used in theanalysis. Size pattern approaches then may not require additionalsequencing to provide more reads in a certain size range. Moreover, evenwith higher sequencing depth at certain low levels of fetal fraction,approaches that do not use size bands or size patterns may still notaccurately determine trisomy 21. The low fetal fraction may not resultin a statistically significant size difference between trisomy 21 and aeuploidy case if size bands or size patterns are not analyzed. Moreover,while existing approaches using size selection without size bands orsize patterns may be used to complement other techniques, embodimentsusing size bands or size patterns may be used independently to determinetrisomy 21 or a copy number aberration.

In this study, we developed a novel method to allow NIPT to be performedfor a pregnant woman with a low fetal DNA fraction, for exampleextending to 2%. With more samples used to train a neural network modelor other machine learning model, we would expect to further lower thelimit of detection. We took advantage of the fact that the degree ofcopy number changes in maternal plasma DNA would exhibit distinctpatterns in relation to different size bands between pregnancies withtrisomic and euploid fetuses. This is an important step to achieve abroad population coverage by lowering the limit of non-invasivedetection of fetal chromosomal aneuploidies extending to a fetal DNAfraction of below 2%. Using conventional approaches, pregnanciesinvolving a fetal DNA fraction of below 4% were not suitable for NIPTand generally would be issued with a non-reportable result or testfailure.

Our new approach has potential not only to reduce the false negativerate because of the lower limit of detection, but also to improve actualPPVs because there were a number of reports showing that the risk ofcarrying aneuploidies would increase in those pregnancies with a fetalDNA fraction below 4% (Norton et al. N. Engl. J. Med. 2015;372:1589-1597). Previously, some workers argue that pregnancies with lowfetal DNA fraction should receive genetic counseling and be offeredcomprehensive ultrasound evaluation and diagnostic testing because of anincreased risk of aneuploidy (Yaron Prenat. Diagn. 2016; 36:391-396).Since the fetal DNA fraction is generally inversely correlated withmaternal weight (Wang et al. Prenat. Diagn. 2013; 33:662-666; Hudecovaet al. PLoS One 2014; 9:e88484), the pregnancies with high body massindex would particularly benefit from the ability of such a size-bandbased approach to sensitively tackle the scenarios with a low fetal DNAfraction. Another use of our new approach would be to allow NIPT to beperformed earlier in gestation (e.g. before 10 weeks of gestation), whenthe fetal DNA fractions are generally lower.

D. Methylation Level Analysis in Oncology

Copy number aberrations (CNA) are also present with many cancers. As aresult, CNAs may be used to determine a level of cancer in a subject. Inaddition, cancer patients often show higher levels of methylation incertain genomic regions. Methylation markers therefore may also be usedin combination with size band analysis to determine the level of cancer.

1. Size Pattern Analysis with Methylation

We reasoned that other types of cancer associated aberrations such asmethylation would be also able to be used for constructing the specificsize-band based patterns which could be differentiated from thenon-cancer subjects. Therefore, we also further analyzed 4 plasma DNAsamples from HCC patients as mentioned above. We used, but are notlimited to, targeted bisulfate sequencing to quantify the methylationlevels for those regions that are supposed to be unmethylated in organsof healthy subjects but that have a much higher chance of beingmethylated in cancer patients. We applied the size-band based approachdescribed herein to explore the size-band associated patterns in termsof methylomic aberrations in comparison with the healthy subjects.Methylation is described further in U.S. application Ser. No.13/842,209, filed Mar. 15, 2013 (issued as U.S. Pat. No. 9,732,390 onAug. 15, 2017) and U.S. application Ser. No. 14/803,692 filed Jul. 20,2015, the contents of both are incorporated herein by reference for allpurposes.

FIG. 7 shows size-band based changing patterns of the measuredmethylation in plasma DNA of hepatocellular carcinoma (HCC) patients.The z-scores are calculated by calculating a mean average methylationlevel for reference samples from healthy subjects known not to have HCCand calculating the standard deviation associated with the averagemethylation level. The z-score at each size band is calculated as thedifference between the methylation level at that size band and the meanaverage methylation level, and the difference divided by the standarddeviation. The dashed lines in FIG. 7 indicate a z-score of +3 or −3,which may be used to show statistical significance from the mean averagemethylation level.

Red or darker lines 702, 704, 706, and 708 represented early HCC (eHCC)and gray lines represented the chronic hepatitis B virus (HBV) carrierswithout HCC. In FIG. 7, we could ascertain distinct size-band patternsof methylomic abnormalities associated with HCC patients (lines 702,704, 706, and 708), which allowed for identifying cancer patients fromHBV carriers (gray lines) in HCC01, HCC02 and HCC03. Lines 702, 704, and706 show patterns that have at least two peaks that appear considerablyhigher from the gray lines for HBV samples. Line 708 is closer to thegray lines but still has two peaks higher than the gray lines for theHBV samples. The right-most data in each graph, labeled “All,” is thepooled z-score for all data, regardless of size-band. For HCC04, thenon-random size-band based curving patterns turned out to be moreinformative than the overall degree of aberrant methylations with theuse of all fragments (represented by circle 710). Different genomicregions were used in the different graphs. Chromosomal arm 1q was usedfor HCC01 and HCC04, 10p was used for HCC02, and 19q was used for HCC03.In other embodiments, size-band based changing patterns of, for examplebut not limited to, hypomethylation, point mutations,hydroxymethylation, fragmentation ends, etc. could be also used fordetecting cancers.

2. Example Method for Determining a Level of Cancer

FIG. 8 shows a method 800 of determining a level of cancer in abiological sample from a subject. The biological sample may include amixture of cell-free DNA molecules. The cell-free DNA molecules mayinclude tumor DNA molecules and non-tumor DNA molecules.

At block 802, method 800 may include measuring a first amount ofmethylated cell-free DNA molecules from the biological samplecorresponding to a size range for each size range of a plurality of sizeranges. The methylated cell-free DNA molecules may be from a chromosomalarm. Measuring amounts of methylated cell-free DNA moleculescorresponding to a size range may be performed as described in method600 or any other method described herein, except that the cell-free DNAmolecules are methylated. The first amount of methylated cell-free DNAmolecules may be from one or more genomic regions. A genomic region maybe a chromosomal arm, e.g., 1p, 1q, 8p, 8q, 13q, or 14p. Variouscombinations of genomic regions may be used. The particular regions touse can be determined by analyzing accuracy for various combinations ofregions for determining a level of cancer on a training set of sampleshaving a known level of cancer.

At block 804, method 800 may include calculating for each size range, bya computer system, a methylation level using the first amount ofmethylated cell-free DNA molecules corresponding to the size range and asecond amount of DNA molecules in a second size range that includessizes not in the size range. The second amount may be of methylatedcell-free DNA molecules. In these or other embodiments, the secondamount may include non-methylated cell-free DNA molecules.

The methylation level may be a z-score or a normalized amount of DNAmolecules (e.g., a fraction, a percentage, or a relative abundance) ofDNA molecules that are methylated or unmethylated at one or more sites.For example, the methylation level may be a ratio of the first amount tothe second amount. In other embodiments, the methylation level may be az-score. The z-score may be calculated using a ratio of the amount ofcell-free DNA molecules corresponding to the size range to the secondamount. The difference between the calculated ratio and a mean averageratio is then divided by the standard deviation to determine thez-score. The mean average ratio may be an average methylation level fora control group (e.g., non-cancer patients, reference samples, orgenomic region not associated with cancer). If the methylation level isa z-score, a methylation level for a size range may be any point onlines 702, 704, 706, and 708 in FIG. 7.

At block 806, method 800 may include obtaining a reference size patternincluding a plurality of reference methylation levels for the pluralityof size ranges. The plurality of size ranges may be determined by amachine learning algorithm and may be determined in the same way asdescribed for method 600. The reference size pattern may be determinedfrom a plurality of reference samples from subjects with cancer or fromsubjects without cancer. For example, the reference samples may be frompatients known not to have HCC or any type of cancer. The reference sizepattern may be based on data from chronic HBV carriers without HCC. Forexample, the reference size pattern may be any of the gray lines for HBVin FIG. 7. In some embodiments, the reference size pattern may be astatistical representation of all the size patterns for the referencesamples, as explained with method 600.

At block 808, method 800 may include comparing a plurality of themethylation levels to the reference size pattern. Method 800 may includecomparing each methylation level of the plurality of size ratios to thereference methylation level at the corresponding size range. Comparingthe methylation levels to the reference size pattern may be performed inthe way the size ratios are compared to the reference size pattern inmethod 600, except with methylation levels in place of size. Method 800may include determining that each methylation level is statisticallysimilar to the reference methylation level at the corresponding sizerange. In some embodiments, method 800 may include determining that eachmethylation level or some methylation levels are statistically differentto the reference methylation level at the corresponding size range.

In some embodiments, comparing the plurality of methylation levels tothe reference size pattern may include determining a size patternincluding the plurality of methylation levels for the plurality of sizeranges. The size pattern may be compared to the reference size pattern.The size pattern may be determined to have a similar shape as thereference size pattern. Comparisons to a reference size pattern inmethod 800 may be analogous to comparisons to the reference size patternin method 600.

If the first amount of methylated cell-free DNA molecules are from morethan one genomic region, the methylation levels may be analyzed based ontheir location in the genome. The plurality of methylation levels mayinclude a multi-dimensional vector. The multi-dimensional vector may beN×M with N being the number of size ranges and M being the number ofgenomic regions. A genomic region may be a chromosome, a chromosomalarm, or a portion of a chromosomal arm. The reference size pattern maysimilarly be a multi-dimensional vector (e.g., size N×M). The pluralityof methylation levels may be compared to the reference size patternusing machine learning models or other techniques. The use ofmulti-dimensional vectors and methylation levels is described below(e.g., FIGS. 13, 14A, 14B, and 14C).

At block 810, method 800 may include determining a level of cancer basedon the comparison. The level of cancer may include whether the subjecthas or does not have cancer, a likelihood of cancer, or a tumor size.

If the reference size pattern is determined from the plurality ofreference samples from subjects with cancer and the comparison includesa determination of similar methylation levels or a similar shape, thenthe subject may be determined to have cancer. With this reference sizepattern, if the comparison includes a determination of differentmethylation levels or a different shape, then the subject may bedetermined to not have cancer. If the reference size pattern isdetermined from a plurality of reference samples without cancer and thecomparison includes a determination of different methylation levels orshape, then the subject may be determined to have cancer. And if thereference size pattern is determined from a plurality of referencesamples without cancer and the comparison includes a determination ofsimilar methylation levels or shape, then the subject may be determinedto not have cancer.

E. Pattern Analysis with Size-Banded Matrix

With various cancers, certain genomic regions, including chromosomalarms, may be more likely to have copy number aberrations. Analyzing thesize ranges by chromosomal arm for possible copy number aberrations maythen be used to help determine a probability of cancer or detect cancer.Machine learning models can be used to determine a cancer classifierbased on a pattern of size characteristics at different chromosomalregions (e.g., arms).

1. Size Pattern Analysis

Because the size profile of tumor-derived DNA in the plasma of cancerpatients has been shown to be different from nontumor-derived DNAmolecules, with the former generally comprising of more short DNAmolecules (Jiang et al. Proc. Natl. Acad. Sci. 2015; 112:E1317-E1325),we reasoned that the size-band based approach described in thisinvention would be useful for detecting cancer-associated aberrations,such as copy number aberrations (CNA) and methylomic aberrations. As anexample, we applied size-band based pattern recognition to 4 plasma DNAsamples of early hepatocellular carcinoma (HCC) patients and 67 chronichepatitis B (HBV) carriers without HCC cancers (HBV carriers). Thirtyplasma DNA samples of healthy controls were used to build the normalreference range of copy number changes which was used to call the CNAsand methylomic aberrations in HCC patients and HBV carriers.

FIG. 9 shows size-band based changing patterns of the measured copynumber aberrations in plasma DNA of hepatocellular carcinoma (HCC)patients. Red lines represented early HCC (eHCC) and gray linesrepresented the chronic hepatitis B virus (HBV) carriers without HCC. Weobserve that the curve (red or darker lines 902, 904, 906, and 908) ofsize-band patterns of measured CNAs in patients with HCC cancers weredistinct from those curves (gray lines) for patients with HBV carriers.For example, HCC01 and HCC03 cases had copy gains on 13q and 1pchromosomal arms, respectively.

In HCC01 and HCC03, we could consistently detect the non-randomwave-like size-band based patterns in which size bands with themid-point at 210 bp tended to a turning point relative to its left andright sides showing copy number changes and the size-band patternsaround 120 bp showed a tendency of “bell curve.” For the HCC02 case thatsubjected to 14q deletions, an inverted “bell curve” were present. Forthe HCC04 case, if we used a z-score for all the fragments, we could notdetect the cancer, as shown by circle 910 having a z-score below 3 andwell within the range of z-scores for the non-cancer patients. However,if we utilized the size-band based approach, we could distinguish HCC04from the non-cancer patients showing a random size-band based patterns(gray lines). In contrast, such non-random distinct size-band basedpatterns were not present in the control group. Different chromosomalarms show different size patterns. A size pattern may need to bereferenced to a size pattern specific to a chromosomal arm.

2. Cancer Classifier with Size-Banded GR Matrix

Cancer cells generally bear the copy number aberrations that would occurin any chromosomal arms, which would be reflected in blood plasma whentumor cells shed DNA into the blood circulation of a cancer patient.Because the tumor-derived cell-free DNA molecules are shown to havedistinct size properties in comparison to background normal cell-freeDNA (e.g., tumor cell-free DNA molecules are shorter than backgroundcell-free DNA derived from normal cells), the relative tumor DNAfraction across different size ranges would be varied. Thus, themeasured degree of copy number aberrations across different size rangespresent in plasma of a cancer patient would be a function of therelative tumor DNA fraction across different size ranges.

We proposed that to capture the detailed patterns of the measured copynumber aberrations across different size ranges would improve theperformance in differentiating cancer and non-cancer patients. Thepatterns can include multiple regions as well.

FIG. 10 illustrates a workflow for a size-banded genomic representation(GR) approach for cancer detection according to embodiments of thepresent invention. At stage 1010, we mapped the sequenced cell-free DNAfragments to reference genome. At stage 1020, the sequenced fragmentsare mapped to different chromosomal arms.

At stage 1030, the sequenced fragments are further classified intodifferent size ranges (size bands). For example, the size ranges mayinclude, but are not limited to, 35-75 bp, 40-80 bp, 45-85 bp, 50-90 bp,55-95 bp, 60-100 bp, 65-105 bp, 70-110 bp, 75-115 bp, 80-120 bp, 85-125bp, 90-130 bp, 95-135 bp, 100-140 bp, 105-145 bp, 110-150 bp, 115-155bp, 120-160 bp, 125-165 bp, 130-170 bp, 135-175 bp, 140-180 bp, 145-185bp, 150-190 bp, 155-195 bp, 160-200 bp, 165-205 bp, 170-210 bp, 175-215bp, 180-220 bp, 185-225 bp, 190-230 bp, 195-235 bp, 200-240 bp, 205-245bp, 210-250 bp, 215-255 bp, 220-260 bp, 225-265 bp, 230-270 bp, 235-275bp, 240-280 bp, 245-285 bp, 250-290 bp, 255-295 bp, 260-300 bp, 265-305bp, 270-310 bp, 275-315 bp, 280-320 bp, 285-325 bp, 290-330 bp, 295-335bp, 300-340 bp, 305-345 bp, 310-350 bp, 315-355 bp, 320-360 bp, 325-365bp, 330-370 bp, 335-375 bp, 340-380 bp, 345-385 bp, 350-390 bp, 355-395bp, 360-400 bp, 365-405 bp, 370-410 bp, 375-415 bp, 380-420 bp, and385-425 bp. Such size ranges may be used for all other embodiments aswell.

For a group of molecules within a particular size range, the proportionof sequenced fragments mapped to each chromosomal arm would becalculated, herein being referred to as genomic representation (GR). GRis the proportion of all the DNA fragments that correspond to aparticular region (or entire genome) within the size range. Stage 1030shows GR for different size ranges, for different chromosomal arms, forsamples known to have cancer and for samples known to not have cancer.

As an example, if each chromosomal arm includes 71 size ranges andautosomes have a total of 39 chromosomal arms, then the size ranges andthe chromosomal arms result in a 2,769-dimensional vector. Stage 1040shows a table (“Size-banded GR matrix”) that shows possiblemultidimensional vectors. First row 1042 corresponds to Cancer Sample 1and shows a 71×N dimensional vector, where N is the number ofchromosomal arms. The table shows M samples for cancer and P samples fornon-cancer.

At stage 1050, the multi-dimensional vectors and a size-banded GR matrixformed from the multi-dimensional vectors can be used to train a cancerclassification model. The machine learning algorithms or deep learningalgorithms could be used for training the cancer classifier, includingbut not limited to support vector machines (SVM), decision tree, naiveBayes classification, logistic regression, clustering algorithm,principal component analysis (PCA), singular value decomposition (SVD),t-distributed stochastic neighbor embedding (tSNE), artificial neuralnetwork, as well as ensemble methods which construct a set ofclassifiers and then classify new data points by taking a weighted voteof their predictions. Once the cancer classifier is trained, theprobability of cancer for a new patient can be predicted.

The training data can include cancer and non-cancer subjects. Machinelearning algorithms modeling the cell-free DNA measurements (size-bandedGR, methylation, and so on) can be used to construct a classifyingboundary (e.g., using a set of trained weights and coefficientsorganized in linear or non-linear formula, such as logistic regressionformula) which give a best separation between cancer and non-cancersubjects. The deviation of an input vector of a new sample including thecell-free DNA measurements from an optimal classifying boundary towardcancer-associated data points would indicate the likelihood of beingcancer. Such deviation could be normalized or translated intoprobability of cancer within a scale of from 0 to 1. The higher theprobability, the higher likelihood of being cancer. The probability ofcancer above a certain threshold (e.g. >0.6) can be considered as apositive test with cancer.

For hepatocellular carcinoma, it was reported that 1p, 1q, 8p, and 8qwere commonly aberrant in terms of copy numbers (Proc Natl Acad Sci USA.2015 Mar 17;112(11):E1317-25). Thus, to illustrate the performance ofsize-banded cancer detection, we used massively parallel sequencingplatform to sequence a number of healthy controls (CTR), HBV carriers(HBV), cirrhotic subjects (cirrhosis), early-stage HCC (eHCC),intermediate-stage HCC (iHCC), and advanced-stage HCC (aHCC). For thetraining dataset, we sequenced a limited number of advanced stage HCCpatients, and then artificially admixed the sequencing results ofadvanced-stage HCC patients with those of non-HCC subjects to form thetraining dataset containing enough HCC positive patients with the widecoverage of tumor DNA fractions ranged from 0.01% and 50% and non-HCCsubjects. To this end, 401 HCC patients were created by randomlyrepeatedly mixing 34 HBV, 10 CTR and 9 aHCC subjects by varying theproportion of sequencing reads being used, and 175 non-HCC patients werecreated by randomly repeatedly mixing 34 HBV, 15 Cirrhosis, and 10 CTRsubjects. SVM algorithm was used to train the cancer classifier usingsuch 401 HCC patients and 175 in-HCC patients.

At stage 1060, the trained cancer classification model can be used topredict whether a new sample has cancer or does not have cancer. Aprobability of cancer may be determined by the model, with a probabilityabove the threshold considered as a positive test for cancer.

The size-banded approach for detecting cancer and the conventionalz-score approach were applied to a testing dataset including 30 CTR, 19HBV, 14 cirrhosis, 36 eHCC, and 11 iHCC subjects.

FIG. 11A shows the results of the size-banded approach for detectingcancer. SVM was used to train the cancer classifier. Both eHCC and iHCCsubjects had median values above a 0.60 probability of cancer, with iHCChaving a higher probability than eHCC. CTR, HBV, and cirrhosis subjectsshowed median probabilities below 0.20. The size-banded approach fordetecting cancer had 64% sensitivity at the specificity of 95%. Thedotted red line corresponds to 95% specificity.

FIG. 11B shows the results of the conventional z-score approach fordetecting cancer. The dotted red line corresponds to 95% specificity,which was at a z-score around 4.2. Chromosomal arms 1p, 1q, 8p, and 8qwere used as examples. The GR for each arm of a test sample wascalculated. The corresponding mean and standard deviation was alsocalculated. Each arm z-score would be calculated as (GR−mean)/standarddeviation. The absolute z-score equaled the sum of the four absolutez-scores corresponding to the four chromosomal arms. The iHCC subjectshad a median absolute z-score of cancer noticeably higher than CTR, HBV,cirrhosis, and eHCC subjects. While the median absolute z-score for iHCCwas higher than absolute z-scores for the other subjects, the z-scoresof several iHCC subjects were fairly similar to the other subjects.However, the median absolute z-score for eHCC was only slightly higherthan those of CTR, HBV, and cirrhosis subjects and was about the same asa z-score threshold level of 3. The conventional z-score approach had51% sensitivity at the specificity of 95%. Thus, the size-bandedapproach shows superior sensitivity over the conventional z-scoreapproach.

FIG. 11C shows the superiority of the size-banded approach over theconventional z-score approach with a receiver operating characteristiccurve (ROC) analysis (0.84 vs. 0.82).

3. Example Method with Size-Banded Genomic Representation (GR) Matrix

FIG. 12 shows an example method 1200 of determining a cancerclassification in a biological sample from a subject. The biologicalsample may include a mixture of cell-free DNA molecules including tumorDNA molecules and non-tumor DNA molecules.

At block 1202, a first amount of cell-free DNA molecules from abiological sample may be measured. The first amount of cell-free DNAmolecules may correspond to each size range for M ranges and to eachgenomic region for N genomic regions. The plurality of size ranges maybe determined as described with method 600 or method 800. Each genomicregion may be a chromosomal arm.

At block 1204, a size ratio may be calculated using the first amount ofcell-free DNA molecules and a second amount of cell-free DNA moleculesin a second size range that includes sizes not in the size range. Thesize ratio may be calculated as in method 600, but the size ratio may befor a particular genomic region (e.g., chromosomal arm). As an example,the size ratio may be any of genomic representations GR1, GR2, GR3, GR71 in row 1004 in FIG. 10. Calculating the size ratio may generate ameasurement vector of N×M size ratios. N may be an integer greater thanequal to 1. N and M may be integers greater than 1, including greaterthan 2, 3, 4, 5, or 6.

At block 1206, a reference size pattern may be obtained. The referencesize pattern may include a reference vector of reference size ratios forthe N genomic regions and the M size ranges. The reference size patternmay be determined from a plurality of reference samples from subjectswith cancer or from subjects without cancer. The reference size patternmay be determined using a machine learning model.

The machine learning model may be determined using a training set ofsize ratios including size ratios at each of the plurality of genomicregions from an individual having cancer. The cancer classifier may bedetermined using a machine learning algorithm or deep learningalgorithm. The machine learning model or deep learning algorithm mayinclude support vector machines (SVM), decision tree, naive Bayesclassification, logistic regression, clustering algorithm, principalcomponent analysis (PCA), singular value decomposition (SVD),t-distributed stochastic neighbor embedding (tSNE), artificial neuralnetwork, or any algorithm described herein. The training set may includesize ratios at different genomic regions for individuals determined tohave cancer and for individuals determined not to have cancer. Themachine learning model may be the cancer classifier in FIG. 10.

At block 1208, the measurement vector may be compared to the referencevector. The comparison may be compared using a machine learning model.The comparison may result in a value based on the similarity of themeasurement vector to the reference vector.

Comparing the measurement vector to the reference vector may includecomparing the N×M size ratios to a plurality of threshold values thatare determined from the plurality of reference samples. For example,each size range may have a different threshold value, which may be basedon a standard deviation for reference samples. Accordingly, there may beN×M threshold values. A single size range may also have differentthreshold values, with each threshold value associated with a differentcertainty level that the size ratio is different from the referencesamples. Comparing may include counting the number of threshold valuesexceeded and determining the level of cancer based on the comparison. Ahigher level of threshold values exceeded may indicate a largerdifference between the measurement vector and the reference vector.

At block 1210, a level of cancer may be determined based on thecomparison. The cancer may include hepatocellular carcinoma. The cancermay include colorectal cancers, lung cancers, nasopharyngeal cancers,ovarian cancers, stomach cancers, and blood cancers. Method 1200 mayallow for differentiation between cancers and non-cancer subjects. Thesubject may be classified as having cancer or having a high likelihoodof cancer based on the value based on the similarity of the measurementvector to the reference vector. The value based on the similarity may becompared to the cutoff value. A value based on the similarity that moregreatly exceeds the cutoff value may indicate a higher likelihood orseverity of cancer. The method may further comprising treating cancerwhen the subject is classified as having cancer or having a highlikelihood of cancer.

Method 1200 may be adapted to determine a level of an autoimmunedisorder instead of cancer. An autoimmune disorder may include systemiclupus erythematosus (SLE). The sizes DNA fragments have been found to berelated to SLE, as described in US Patent Publication No. 2015/0087529A1, filed Sep. 19, 2014, the contents of which are incorporated hereinby reference for all purposes. A level of the autoimmune disorder may bedetermined by comparing measurement vectors to a reference vector. Thereference vector may be from a reference size pattern. The referencesize pattern may be determined from samples from healthy subjects orsubjects with known levels of the autoimmune disorder. Method 1200 mayallow for differentiation between subjects with and without autoimmunedisorders.

4. Cancer Classifier with Size-Banded Methylation Density (MD) Matrix

Cancer cells generally bear the specific methylation patterns whichwould occur in any genomic regions. For example, in cancer cells, Alurepeat regions may be preferentially less methylated compared withnon-malignant cells, and CpG island regions may be preferentially moremethylated compared with non-malignant cells. Such cancer-associatedaberrant methylation signals can be reflected in blood plasma of cancerpatients when tumor cells shed DNA into the blood circulation. Asexplained above, the relative tumor DNA fraction across different sizeranges varies. Thus, the measured degree of cancer-associatedmethylation levels across different size ranges present in plasma of acancer patient would be a function of the relative tumor DNA fractionacross different size ranges.

We proposed that to capture the detailed patterns of the measuredmethylation aberrations across different size ranges would improve theperformance in differentiating cancer and non-cancer patients.

FIG. 13 illustrates a workflow for a size-banded methylation density(MD) approach for cancer detection according to embodiments of thepresent invention. At stage 1310, we mapped the sequencedbisulfite-converted cell-free DNA fragments to a reference genome usingMethy-Pipe (Jiang et al., PLoS One. 2014;9(6):e100360) or othermethylation-aware aligners. At stage 1320, the sequenced fragmentsmapped to different differentially methylated regions are located.

At stage 1330, the sequenced fragments are further classified intodifferent size ranges (size bands). For example, the size ranges mayinclude any size ranges described herein, including those size rangesdescribed in stage 1030 for FIG. 10.

For a group of molecules within a particular size range, the proportionof sequenced CpG on a region of interest (e.g., Alu repeat or CpGislands) would be calculated, resulting in the methylation density (MD).which reflects the methylation level. Regions may show differentmethylation levels between liver cancer cells and other normal cells,including hematopoietic cells (e.g. T cells, B cells, neutrophils,macrophages, erythroblast cells, and so on), liver cells, and coloncells. Stage 1330 shows MD for different size ranges, for differentgenomic regions, and for samples known to have cancer and for samplesknown to not have cancer.

As an example, if each region includes 71 size ranges and there are atotal of 32,450 regions showing differentially methylated in betweenliver cancer cells and other normal cells, then the size ranges and thegenomic regions result in a 2,303,950-dimensional vector. Stage 1340shows a table (“Size-banded MD matrix”) that shows possiblemultidimensional vectors. First row 1342 of the table corresponds toCancer Sample 1 shows a 71×N dimensional vector, where N is the numberof genomic regions. The table shows M samples for cancer and P samplesfor non-cancer.

At stage 1350, the multi-dimensional vectors and a size-banded MD matrixformed from the multi-dimensional vectors can be used to train a cancerclassification model. Training can be by any suitable machine learningmodel that performs a classification, e.g., as described herein,including for stage 1050 of FIG. 10. Once the cancer classifier istrained, the probability of a sample indicating cancer for a new patientcan be predicted. The probability of cancer being above a certainthreshold (e.g. >0.6) can be considered as a positive test with cancer.

To illustrate the performance of cancer detection with the use ofsize-banded methylation levels, we used massively parallel sequencingplatform to sequence a number of healthy controls (CTR), HBV carriers(HBV), cirrhotic subjects (cirrhosis), early-stage HCC (eHCC),intermediate-stage HCC (iHCC), and advanced-stage HCC (aHCC). For thetraining dataset, we sequenced a limited number of advanced stage HCCpatients, and then artificially admixed the sequencing results ofadvanced-stage HCC patients with those of non-HCC subjects to form thetraining dataset containing enough HCC positive patients with the widecoverage of tumor DNA fractions ranged from 0.01% and 50% and non-HCCsubjects. To this end, 140 HCC patients were created by randomlyrepeatedly mixing 27 HBV and 7 aHCC subjects by varying the proportionof sequencing reads being used, and 140 non-HCC patients was created byrandomly repeatedly mixing 7 HBV and 20 CTR subjects. SVM algorithm wasused to train the cancer classifier using such 140 HCC patients and 140non-HCC patients.

At stage 1360, the trained cancer classification model can be used topredict whether a new sample has cancer or does not have cancer. Aprobability of cancer may be determined by the model, with a probabilityabove the threshold considered as a positive test for cancer.

FIGS. 14A, 14B, and 14C show a comparison between size-banded MD andconventional z-score approaches according to embodiments of the presentinvention. FIG. 14A shows results for the size-banded MD approach. FIG.14B shows results for the conventional z-score approach.

FIGS. 14A and 14B show that in a testing dataset including 27 HBV, 36eHCC, and 11 iHCC subjects, the size-banded methylation approach fordetecting cancer was superior to the conventional z-score approach. Theconventional z-score approach was conducted in the following way: (1)the pooled methylation level (denoted by “X”) for total fragmentsderived from all regions of interest are calculated; (2) the mean of thepooled methylation levels (M), and the standard deviation of the pooledmethylation levels (SD) in a non-cancer group are calculated; (3) thenthe conventional methylation z-score is defined by: z-score=(X-M)/SD.SVM was used to train the cancer classifier. The size-banded methylationapproach in FIG. 14A had a 74.5% sensitivity at the specificity of92.5%. By contrast, the conventional z-score approach in FIG. 14B hadlower sensitivity, 65.9% sensitivity at the specificity of 92.5%. Theincreased sensitivity may lead to important benefits. Early detection ofearly cancers is generally associated with better treatment outcomes.Both the eHCC and iHCC groups are considered to be treatable stages.Therefore, any increase in sensitivity in the treatable cases has aclinical impact and may translate to very different survival profilesfor the patients.

FIG. 14C shows the superiority of size-banded methylation approach inthe receiver operating characteristic curve (ROC) analysis (SVM: 0.89AUC vs. z-score: 0.87 AUC).

Accordingly, the use of multi-dimensional vectors with genomicrepresentation (GR) (e.g., FIGS. 10-12) can be adapted for analysisusing methylation densities in place of GR.

F. Additional Size Pattern Applications

Size-band based patterns would inform the origin for those aberrationsseen in plasma DNA. As an example, in a pregnancy context, if the copynumber aberrations derived from the mother, the size-band patterns wouldoccur in a reverse direction compared with those originating from thefetus because maternal DNA fragments are longer than fetal DNA (Yu etal. Clin. Chem. 2017; 63:495-502). Size-band based molecular diagnosticscould also be applied to the analysis of cell-free DNA in other clinicalconditions, such as cancer (Jiang et al. Proc. Natl. Acad. Sci. 2015;112:E1317-E1325), including enhancing the detection of point mutations,sub-chromosomal aberrations and epigenetic abnormalities. A clinicalcondition may include determining the presence of an immuno-response toa transplanted tissue or organ.

Besides, it would also allow us to distinguish the plasma DNAconfounding aberrations present in plasma DNA such as systemic lupuserythematosus (SLE) because the apparent copy number changes present inplasma DNA of SLE patients (Chan et al. Proc. Natl. Acad. Sci. 2014;111:E5302-E5311) would be likely due to preferential binding of anti-DNAantibody to particular DNA sequences rather than a true copy numberchanges in particular cells. Thus, size-band based analysis would beexpected to see random shape changes in relation to different size bandsfor measured copy number aberrations present in plasma of SLE patients.

Embodiments may include treating the disease or condition in the patientafter determining the level or probability of the disease or conditionin the patient. Treatment may include any suitable therapy, drug, orsurgery, including any treatment described in a reference mentionedherein. Information on treatments in the references are incorporatedherein by reference.

III. Materials and Methods Sample Collection and Processing

The anonymized data analyzed for this retrospective study were obtainedfrom existing patient data in the University Pathology Service (UPS) ofThe Chinese University of Hong Kong. Patient data consisting of 161samples were generated as a result of the UPS laboratory-developed test.Anonymized patients with HCC admitted to the Department of Surgery ofthe Prince Wales Hospital, Hong Kong, for tumor resection wererecruited. All blood was collected before surgery. Anonymized HBVcarriers and cirrhosis subjects were recruited from the Department ofMedicine and Therapeutics of the Prince of Wales Hospital, Hong Kong.The samples were obtained by centrifuging blood to obtain plasma.Briefly, peripheral blood samples were collected into EDTA-containingtubes, which were subsequently centrifuged at 1,600 g for 10 min at 4°C. The plasma portion was recentrifugated at 16,000 g for 10 min at 4°C. to obtain cell-free plasma that were stored at −80° C. until furtheranalysis. DNA was extracted from 4-10 mL of plasma using the QIAamp DSPDNA Blood Mini Kit (Qiagen). The plasma DNA was concentrated with aSpeedVac Concentrator (Savant DNA120; Thermo Scientific) into a 75-μLfinal volume per sample.

Sequencing Library Preparation and DNA Sequencing

Using the extracted plasma DNA, indexed DNA libraries were constructedwith the Paired-end Sequencing Sample Preparation Kit according to themanufacturer's instructions. In this step, plasma double-stranded DNAmolecules would be end-repaired to form the blunt ends andsimultaneously were added an extra A base. The adaptors, which can aidPCR amplification, be annealed to flowcell, and facilitate sequencing,were ligated to A-tagged double-stranded plasma DNA molecules to formthe sequencing library. The library can be sequenced in a paired-endmode with the use of 36 or 50 or 75 cycles for each end as previouslydescribed (Yu et al. Proc. Natl. Acad. Sci. U.S.A. 2014; 111:8583-8).

Sequence Alignment

Sequences from each samples were aligned to the human reference genome(hg19) using the Short Oligonucleotide Alignment Program 2 (SOAP2) (Liet al. Bioinformatics 2009; 25:1966-1967) as previously described (Yu etal. Proc. Natl. Acad. Sci. U.S.A. 2014; 111:8583-8). On average, eachsample obtained 12 million uniquely mapped paired-end reads (range:10-15 million).

Methylation Levels

The methylation status of sites of the sequence read can be obtained asdescribed herein. For example, the DNA molecules can be analyzed usingsequence reads of the DNA molecules, where the sequencing ismethylation-aware. For example, methylation-aware sequencing caninclude, but not limited to bisulfate sequencing, or sequencing precededby methylation-sensitive restriction enzyme digestion,immunoprecipitation using anti-methylcytosine antibody or methylationbinding protein, or single molecule sequencing that allows elucidationof the methylation status. Other methylation-aware assays can also beused.

The sequence reads can each include a methylation status of cell-freeDNA molecules from the biological sample. The methylation status caninclude whether a particular cytosine residue is 5-methylcytosine or5-hydroxymethylcytosine. The sequence reads can be obtained in variousways, each as various sequencing techniques, PCR techniques (e.g.,real-time or digital), arrays, and other suitable techniques foridentifying sequences of fragments. Real-time PCR is an example ofanalyzing a group of DNA collectively, e.g., as an intensity signalproportional to the number of DNA methylated at a site. A sequence readcan cover more than one site depending on the proximity of the two sitesto each other and the length of the sequence read.

The analysis can be performed by receiving sequence reads from amethylation-aware sequencing, and thus the analysis can be performedjust on data previously obtained from the DNA. In other embodiments, theanalysis can include the actual sequencing or other active steps forperforming the measurements of the properties of the DNA molecules. Thesequencing may be performed in a variety of ways, e.g., using massivelyparallel sequencing or next-generation sequencing, using single moleculesequencing, and/or using double- or single-stranded DNA sequencinglibrary preparation protocols, and other techniques described herein. Aspart of the sequencing, it is possible that some of the sequence readsmay correspond to cellular nucleic acids.

The sequencing may be targeted sequencing, e.g., as described herein.For example, biological sample can be enriched for nucleic acidmolecules from the virus. The enriching of the biological sample fornucleic acid molecules from the virus can include using capture probesthat bind to a portion of, or an entire genome of, the virus. Otherembodiments can use primers specific to a particular locus of the virus.The biological sample can be enriched for nucleic acid molecules from aportion of a human genome, e.g., regions of autosomes. FIG. 1 providesexamples of such capture probes. In other embodiments, the sequencingcan include random sequencing.

After sequencing by a sequencing device, the sequence reads may bereceived by a computer system, which may be communicably coupled to asequencing device that performed the sequencing, e.g., via wired orwireless communications or via a detachable memory device. In someembodiments, one or more sequence reads that include both ends of thenucleic acid fragment can be received. The location of a DNA moleculecan be determined by mapping (aligning) the one or more sequence readsof the DNA molecule to respective parts of the human genome, e.g., tospecific regions, such as differentially methylation regions (DMRs). Inone implementation, if a read does not map to a region of interest, thenthe read can be ignored. In other embodiments, a particular probe (e.g.,following PCR or other amplification) can indicate a location, such asvia a particular fluorescent color. The identification can be that thecell-free DNA molecule corresponds to one of the set of one or moresites, i.e., the particular site may not be known, as the amount of DNAmethylated at one or more sites is all that is needed.

After sequencing and alignment, the methylation status of an individualCpG site could thus be inferred from the count of methylated sequencereads “M” (methylated) and the count of unmethylated sequence reads “U”(unmethylated) at the cytosine residue in CpG context. Using thebisulfite sequencing data, the entire methylomes of maternal blood,placenta and maternal plasma were constructed. The mean methylated CpGdensity (also called methylation density MD) of specific loci in thematernal plasma can be calculated using the equation:

${MD} = \frac{M}{M + U}$

where M is the count of methylated reads and U is the count ofunmethylated reads at the CpG sites within the genetic locus. If thereis more than one CpG site within a locus, then M and U correspond to thecounts across the sites.

As an alternative, a methylation assay can be performed onbisulfite-converted genomic DNA according to an Infinium HD MethylationAssay protocol. The hybridized beadchip can be scanned on an IlluminaiScan instrument. DNA methylation data were analyzed by the GenomeStudio(v2011.1) Methylation Module (v1.9.0) software, with normalization tointernal controls and background subtraction. The methylation index forindividual CpG site can be represented by a beta value (β), which may becalculated using the ratio of fluorescent intensities between methylatedand unmethylated alleles:

$\beta = \frac{{Intensity}\mspace{14mu}{of}\mspace{14mu}{methylated}\mspace{14mu}{allele}}{\begin{matrix}{{{Intensity}\mspace{14mu}{of}\mspace{14mu}{unmethylated}\mspace{14mu}{allele}} +} \\{{{Intensity}\mspace{14mu}{of}\mspace{14mu}{methylated}\mspace{14mu}{allele}} + 100}\end{matrix}}$

Calculation of Fetal DNA Fractions

In pregnancies carrying a male fetus, the fetal DNA fraction (f) in amaternal plasma sample can be determined from the proportion of readsaligned to chromosome Y (% chrY). In a previous study, it was shown thata small number of sequences in the plasma of pregnant women carrying afemale fetus were wrongly aligned to chromosome Y (Chiu et al. Proc NatlAcad Sci USA 2008; 105:20458-20463). Therefore, the % chrY in the plasmaof pregnant women carrying a male fetus was a mixture of the chromosomeY reads derived from the male fetus and the maternal reads that weremisaligned to chromosome Y (Chiu et al. BMJ 2011; 342:c7401). Therelationship between % chrY and fin pregnancies carrying a male fetuscan be expressed using the following equation:

% chrY=% chrY_(male) ×f−% chrY_(female)×(1−f)

where % chrY_(male) is the proportion of reads aligned chromosome Y in aplasma sample containing 100% male DNA, and % chrYfemale is theproportion of reads aligned to chromosome Y in a plasma samplecontaining 100% female DNA.

The specific details of particular embodiments may be combined in anysuitable manner without departing from the spirit and scope ofembodiments of the invention. However, other embodiments of theinvention may be directed to specific embodiments relating to eachindividual aspect, or specific combinations of these individual aspects.

IV. Example Systems

FIG. 15 illustrates a system 1500 according to an embodiment of thepresent invention. The system as shown includes a sample 1505, such ascell-free DNA molecules within a sample holder 1510, where sample 1505can be contacted with an assay 1508 to provide a signal of a physicalcharacteristic 1515. An example of a sample holder can be a flow cellthat includes probes and/or primers of an assay or a tube through whicha droplet moves (with the droplet including the assay). Physicalcharacteristic 1515, such as a fluorescence intensity value, from thesample is detected by detector 1520. Detector can take a measurement atintervals (e.g., periodic intervals) to obtain data points that make upa data signal. In one embodiment, an analog to digital converterconverts an analog signal from the detector into digital form at aplurality of times. Sample holder 1510 and detector 1520 can form anassay device, e.g., a sequencing device that performs sequencingaccording to embodiments described herein. A data signal 1525 is sentfrom detector 1520 to logic system 1530. Data signal 1525 may be storedin a local memory 1535, an external memory 1540, or a storage device1545.

Logic system 1530 may be, or may include, a computer system, ASIC,microprocessor, etc. It may also include or be coupled with a display(e.g., monitor, LED display, etc.) and a user input device (e.g., mouse,keyboard, buttons, etc.). Logic system 1530 and the other components maybe part of a stand-alone or network connected computer system, or theymay be directly attached to or incorporated in a device (e.g., asequencing device) that includes detector 1520 and/or sample holder1510. Logic system 1530 may also include software that executes in aprocessor 1550. Logic system 1530 may include a computer readable mediumstoring instructions for controlling system 1500 to perform any of themethods described herein. For example, logic system 1530 can providecommands to a system that includes sample holder 1510 such thatsequencing or other physical operations are performed. Such physicaloperations can be performed in a particular order, e.g., with reagentsbeing added and removed in a particular order. Such physical operationsmay be performed by a robotics system, e.g., including a robotic arm, asmay be used to obtain a sample and perform an assay.

Any of the computer systems mentioned herein may utilize any suitablenumber of subsystems. Examples of such subsystems are shown in FIG. 16in computer apparatus 1600. In some embodiments, a computer systemincludes a single computer apparatus, where the subsystems can be thecomponents of the computer apparatus. In other embodiments, a computersystem can include multiple computer apparatuses, each being asubsystem, with internal components.

The subsystems shown in FIG. 16 are interconnected via a system bus1675. Additional subsystems such as a printer 1674, keyboard 1678, fixeddisk 1679, monitor 1676, which is coupled to display adapter 1682, andothers are shown. Peripherals and input/output (I/O) devices, whichcouple to I/O controller 1671, can be connected to the computer systemby any number of means known in the art, such as serial port 1677. Forexample, serial port 1677 or external interface 1681 (e.g. Ethernet,Wi-Fi, etc.) can be used to connect computer apparatus 1600 to a widearea network such as the Internet, a mouse input device, or a scanner.The interconnection via system bus 1675 allows the central processor1673 to communicate with each subsystem and to control the execution ofinstructions from system memory 1672 or the fixed disk 1679, as well asthe exchange of information between subsystems. The system memory 1672and/or the fixed disk 1679 may embody a computer readable medium. Any ofthe values mentioned herein can be output from one component to anothercomponent and can be output to the user.

A computer system can include a plurality of the same components orsubsystems, e.g., connected together by external interface 1681 or by aninternal interface. In some embodiments, computer systems, subsystem, orapparatuses can communicate over a network. In such instances, onecomputer can be considered a client and another computer a server, whereeach can be part of a same computer system. A client and a server caneach include multiple systems, subsystems, or components.

It should be understood that any of the embodiments of the presentinvention can be implemented in the form of control logic using hardware(e.g. an application specific integrated circuit or field programmablegate array) and/or using computer software with a generally programmableprocessor in a modular or integrated manner. Based on the disclosure andteachings provided herein, a person of ordinary skill in the art willknow and appreciate other ways and/or methods to implement embodimentsof the present invention using hardware and a combination of hardwareand software.

Any of the software components or functions described in thisapplication may be implemented as software code to be executed by aprocessor using any suitable computer language such as, for example,Java, C++, Python, or Perl using, for example, conventional orobject-oriented techniques. The software code may be stored as a seriesof instructions or commands on a computer readable medium for storageand/or transmission, suitable media include random access memory (RAM),a read only memory (ROM), a magnetic medium such as a hard-drive or afloppy disk, or an optical medium such as a compact disk (CD) or DVD(digital versatile disk), flash memory, and the like. The computerreadable medium may be any combination of such storage or transmissiondevices.

Such programs may also be encoded and transmitted using carrier signalsadapted for transmission via wired, optical, and/or wireless networksconforming to a variety of protocols, including the Internet. As such, acomputer readable medium according to an embodiment of the presentinvention may be created using a data signal encoded with such programs.Computer readable media encoded with the program code may be packagedwith a compatible device or provided separately from other devices(e.g., via Internet download). Any such computer readable medium mayreside on or within a single computer program product (e.g. a harddrive, a CD, or an entire computer system), and may be present on orwithin different computer program products within a system or network. Acomputer system may include a monitor, printer, or other suitabledisplay for providing any of the results mentioned herein to a user.

Any of the methods described herein may be totally or partiallyperformed with a computer system including one or more processors, whichcan be configured to perform the steps. Thus, embodiments can bedirected to computer systems configured to perform the steps of any ofthe methods described herein, potentially with different componentsperforming a respective steps or a respective group of steps. Althoughpresented as numbered steps, steps of methods herein can be performed ata same time or in a different order. Additionally, portions of thesesteps may be used with portions of other steps from other methods. Also,all or portions of a step may be optional. Additionally, any of thesteps of any of the methods can be performed with modules, circuits, orother means for performing these steps.

The above description of example embodiments of the invention has beenpresented for the purposes of illustration and description. It is notintended to be exhaustive or to limit the invention to the precise formdescribed, and many modifications and variations are possible in lightof the teaching above.

In the preceding description, for the purposes of explanation, numerousdetails have been set forth in order to provide an understanding ofvarious embodiments of the present technology. It will be apparent toone skilled in the art, however, that certain embodiments may bepracticed without some of these details, or with additional details.

Having described several embodiments, it will be recognized by those ofskill in the art that various modifications, alternative constructions,and equivalents may be used without departing from the spirit of theinvention. Additionally, a number of well-known processes and elementshave not been described in order to avoid unnecessarily obscuring thepresent invention. Additionally, details of any specific embodiment maynot always be present in variations of that embodiment or may be addedto other embodiments.

Where a range of values is provided, it is understood that eachintervening value, to the tenth of the unit of the lower limit unlessthe context clearly dictates otherwise, between the upper and lowerlimits of that range is also specifically disclosed. Each smaller rangebetween any stated value or intervening value in a stated range and anyother stated or intervening value in that stated range is encompassed.The upper and lower limits of these smaller ranges may independently beincluded or excluded in the range, and each range where either, neither,or both limits are included in the smaller ranges is also encompassedwithin the invention, subject to any specifically excluded limit in thestated range. Where the stated range includes one or both of the limits,ranges excluding either or both of those included limits are alsoincluded.

As used herein and in the appended claims, the singular forms “a”, “an”,and “the” include plural referents unless the context clearly dictatesotherwise. Thus, for example, reference to “a method” includes aplurality of such methods and reference to “the particle” includesreference to one or more particles and equivalents thereof known tothose skilled in the art, and so forth. The invention has now beendescribed in detail for the purposes of clarity and understanding.However, it will be appreciated that certain changes and modificationsmay be practice within the scope of the appended claims.

All publications, patents, and patent applications cited herein arehereby incorporated by reference in their entirety for all purposes.None is admitted to be prior art.

What is claimed is:
 1. A method of determining whether a chromosomalregion exhibits a copy number aberration in a biological sample from asubject, wherein the biological sample includes a mixture of cell-freeDNA molecules including clinically-relevant DNA molecules and other DNAmolecules, the method comprising: for each size range of a plurality ofsize ranges: measuring a first amount of cell-free DNA molecules fromthe biological sample corresponding to the size range, and calculating,by a computer system, a size ratio using the first amount of cell-freeDNA molecules corresponding to the size range and a second amount of DNAmolecules in a second size range that includes sizes not in the sizerange; obtaining a reference size pattern including a plurality ofreference size ratios for the plurality of size ranges, wherein thereference size pattern is determined from a plurality of referencesamples from subjects with a copy number aberration or from subjectswithout a copy number aberration in the chromosomal region; comparing aplurality of the size ratios to the reference size pattern; determiningwhether the chromosomal region exhibits a copy number aberration basedon the comparison.
 2. The method of claim 1, wherein theclinically-relevant DNA molecules comprise fetal DNA or maternal DNA. 3.The method of claim 1, wherein the clinically-relevant DNA moleculescomprise tumor DNA, and the other DNA molecules comprise non-tumor DNA.4. The method of claim 2, wherein the copy number aberration is ananeuploidy.
 5. The method of claim 3, wherein the copy number aberrationis an indication of cancer.
 6. The method of claim 1, wherein each sizerange of the plurality of size ranges are characterized by a bandwidth.7. The method of claim 6, wherein the bandwidth is in a range from 50 bpto 200 bp.
 8. The method of claim 1, wherein each size range isnon-overlapping with any other size range of the plurality of sizeranges.
 9. The method of claim 1, wherein each size range is overlappingwith at least one other size range of the plurality of size ranges. 10.The method of claim 1, wherein the size ratio comprises a z-score. 11.The method of claim 1, wherein the second size range is a range largerthan each size range of the plurality of size ranges.
 12. The method ofclaim 1, wherein the second size range comprises all sizes of cell-freeDNA molecules in the biological sample or all sizes of cell-free DNAmolecules in the chromosomal region.
 13. The method of claim 1, whereinthe cell-free DNA molecules are from a genomic region.
 14. The method ofclaim 13, wherein the genomic region is a chromosome.
 15. The method ofclaim 13, wherein the genomic region is a chromosomal arm.
 16. Themethod of claim 1, wherein: comparing the plurality of the size ratiosto the reference size pattern comprises: comparing each size ratio ofthe plurality of the size ratios to the reference size ratio at thecorresponding size range, determining that each size ratio isstatistically similar to the reference size ratio at the correspondingsize range.
 17. The method of claim 1, wherein: comparing the pluralityof the size ratios to the reference size pattern comprises: determininga size pattern including the plurality of the size ratios for theplurality of size ranges; comparing the size pattern to the referencesize pattern, determining the size pattern has a similar shape as thereference size pattern.
 18. The method of claim 16, wherein: thereference size pattern is determined from the plurality of referencesamples from subjects with a copy number aberration, the method furthercomprising: determining that the chromosomal region exhibits a copynumber aberration based on the comparison.
 19. The method of claim 1,wherein: obtaining the reference size pattern and comparing theplurality of the size ratios to the reference size pattern comprisesinputting the plurality of the size ratios into a machine learningmodel, and the machine learning model was trained using a plurality oftraining size patterns from the plurality of reference samples.
 20. Themethod of claim 1, wherein comparing the plurality of the size ratios tothe reference size pattern comprises comparing the plurality of the sizeratios to a plurality of threshold values that are determined from theplurality of reference samples.
 21. A method of determining a cancerclassification in a biological sample from a subject, wherein thebiological sample includes a mixture of cell-free DNA moleculesincluding tumor DNA molecules and non-tumor DNA molecules, the methodcomprising: for each genomic region of N genomic regions: for each sizerange of M size ranges: measuring a first amount of cell-free DNAmolecules from the biological sample corresponding to the size range andcorresponding to the genomic region, and calculating, by a computersystem, a size ratio using the first amount of cell-free DNA moleculescorresponding to the size range and corresponding to the genomic regionand a second amount of DNA molecules in a second size range thatincludes sizes not in the size range, thereby generating a measurementvector of N×M size ratios, wherein N is an integer greater than or equalto 1, and M is an integer greater than 1; obtaining a reference sizepattern including a reference vector of reference size ratios for the Ngenomic regions and the M size ranges, wherein the reference sizepattern is determined from a plurality of reference samples fromsubjects with cancer or from subjects without cancer; comparing themeasurement vector to the reference vector; and determining a level ofcancer based on the comparison.
 22. The method of claim 21, wherein eachgenomic region is a chromosomal arm.
 23. The method of claim 21,wherein: the reference size pattern is determined using a machinelearning model, wherein the machine learning model comprises at leastone selected from a group consisting of support vector machines,decision tree, naive Bayes classification, logistic regression,clustering algorithm, principal component analysis, singular valuedecomposition, t-distributed stochastic neighbor embedding, andartificial neural network.
 24. The method of claim 21, wherein comparingthe measurement vector to the reference vector comprises using a machinelearning model trained with a training set of training vectorscomprising size ratios for different genomic regions for individualsdetermined to have cancer and for individuals determined not to havecancer.
 25. The method of claim 21, wherein the cancer compriseshepatocellular carcinoma.
 26. The method of claim 21, wherein the levelof cancer comprises a probability of cancer.
 27. The method of claim 21,wherein: obtaining the reference size pattern and comparing themeasurement vector to the reference vector comprises using a machinelearning model, the machine learning model was trained using a pluralityof reference size patterns, comparing the measurement vector to thereference vector comprises determining a cutoff value characterizing thesimilarity of the measurement vector to the reference vector, anddetermining the level of cancer uses the cutoff value.
 28. The method ofclaim 21, wherein comparing the measurement vector to the referencevector comprises comparing the N×M size ratios to a plurality ofthreshold values that are determined from the plurality of referencesamples.
 29. A method of determining a cancer classification in abiological sample from a subject, wherein the biological sample includesa mixture of cell-free DNA molecules including tumor DNA molecules andnon-tumor DNA molecules, the method comprising: enriching the biologicalsample for one or more sizes of the cell-free DNA molecules to form anenriched biological sample; performing methylation-aware sequencing toidentify methylated cell-free DNA molecules in the enriched biologicalsample; for each size range of a plurality of size ranges: measuring afirst amount of the methylated cell-free DNA molecules from the enrichedbiological sample corresponding to the size range, and determining, by acomputer system, a methylation level using the first amount of themethylated cell-free DNA molecules corresponding to the size range and asecond amount of DNA molecules in a second size range that includessizes not in the size range; obtaining, by the computer system, areference size pattern including a reference methylation level for eachsize range of the plurality of size ranges, wherein the reference sizepattern is determined from a plurality of reference samples fromsubjects with cancer or from subjects without cancer; comparing, by thecomputer system, a plurality of the methylation levels to the referencesize pattern; and determining a level of cancer based on the comparison.30. The method of claim 29, wherein the second amount is of methylatedcell-free DNA molecules.
 31. The method of claim 29, wherein themethylated cell-free DNA molecules are from a chromosomal arm.
 32. Themethod of claim 29, wherein: comparing the plurality of the methylationlevels to the reference size pattern comprises: comparing eachmethylation level of the plurality of size ranges to the referencemethylation level at the corresponding size range, determining that eachmethylation level is statistically similar to the reference methylationlevel at the corresponding size range.
 33. The method of claim 29,wherein: comparing the plurality of the methylation levels to thereference size pattern comprises: determining a size pattern includingthe plurality of the methylation levels for the plurality of sizeranges; comparing a slope or an inflection point of the size patternwith a threshold value for a reference slope or a reference inflectionpoint of the reference size pattern, wherein the threshold valueindicates a statistically significant difference between the slope andthe reference slope or the inflection point with the referenceinflection point, based on the comparing, determining the size patternhas a similar shape as the reference size pattern when the slope or theinflection point is not statistically different than the reference slopeor the reference inflection point of the reference size pattern.
 34. Themethod of claim 32, wherein: the reference size pattern is determinedfrom the plurality of reference samples from subjects with cancer, themethod further comprising: determining that the subject has cancer. 35.The method of claim 29, wherein the first amount of the methylatedcell-free DNA molecules are from a genomic region.
 36. The method ofclaim 35, wherein the genomic region is a chromosomal arm, thechromosomal arm selected from the group consisting of 1p, 1q, 8p, 8q,13q, and 14q.
 37. The method of claim 29, wherein comparing theplurality of the methylation levels to the reference size patterncomprises comparing the plurality of the methylation levels to aplurality of threshold values that are determined from the plurality ofreference samples.
 38. The method of claim 29, wherein: the plurality ofsize ranges comprises M size ranges, measuring the first amount of themethylated cell-free DNA molecules comprises measuring the first amountof the methylated cell-free DNA molecules corresponding to the sizerange and corresponding to each genomic region for N genomic regions,calculating the methylation level using the first amount of themethylated cell-free DNA molecules corresponding to the size range andcorresponding to the genomic region and the second amount generates ameasurement vector of N×M methylation levels, wherein N is an integergreater than or equal to 1, and M is an integer greater than 1, thereference size pattern includes a reference vector of referencemethylation levels for the N genomic regions and the M size ranges, andcomparing the plurality of the methylation levels to the reference sizepattern comprises comparing the measurement vector to the referencevector.
 39. The method of claim 29, further comprising: measuring a sizeof each methylated cell-free DNA molecule of the methylated cell-freeDNA molecules by: obtaining sequence reads from both ends of themethylated cell-free DNA molecule, aligning the sequence reads to areference genome to obtain genomic coordinates of the ends of themethylated cell-free DNA molecule, and subtracting the genomiccoordinate of one end from the genomic coordinate of the other end. 40.The method of claim 29, further comprising: measuring a size of eachmethylated cell-free DNA molecule of the methylated cell-free DNAmolecules using sequence reads, wherein the sequence reads are obtainedby massively parallel sequencing.
 41. The method of claim 29, whereinthe methylated cell-free DNA molecules comprise 1,000 molecules.
 42. Themethod of claim 29, wherein the methylation-aware sequencing includesbisulfate sequencing, sequencing preceded by methylation-sensitiverestriction enzyme digestion, immunoprecipitation usinganti-methylcytosine antibody or methylation binding protein, or singlemolecule sequencing.
 43. The method of claim 29, wherein determining themethylation level comprises: calculating a ratio of the first amount tothe second amount, determining a difference between the ratio and anaverage value for a control group, and dividing the difference by astandard deviation for the control group.
 44. The method of claim 29,wherein the plurality of size ranges comprises at least 71 size ranges.45. The method of claim 29, wherein the comparing, by the computersystem, the plurality of the methylation levels to the reference sizepattern comprises using a machine learning model trained using datasetsincluding samples from subjects with cancer and subjects without cancer.46. The method of claim 38, wherein N is at least 4 and M is at least71.